Level 53 • 50/50 questions • 35 seconds per question.
Login to save your score, XP, coins and progress.
What is the common ratio in the sequence \(3,6,12,24,\ldots\)?
A. (2)
सार्व अनुपात \(\frac{6}{3}=2\) है। गुणोत्तर श्रेढ़ी में दूसरा पद पहले पद से भाग दें। / The common ratio is \(\frac{6}{3}=2\). In a geometric progression divide the second term by the first term.
Login to save your score, XP, coins and progress.
If a geometric progression has first term (5) and common ratio (3), what is the fourth term?
C. (135)
\(a_4=5\cdot3^3=135\)। (n)वें पद के लिए \(a_n=ar^{n-1}\) याद रखें। / \(a_4=5\cdot3^3=135\). Remember \(a_n=ar^{n-1}\) for the (n)th term.
Login to save your score, XP, coins and progress.
Which sequence is a geometric progression?
B. \(4,12,36,108,\ldots\)
\(4,12,36,108,\ldots\) में हर बार (3) से गुणा हो रहा है। गुणोत्तर श्रेढ़ी में लगातार अनुपात समान होता है। / In \(4,12,36,108,\ldots\), each term is multiplied by (3). In a geometric progression consecutive ratios are equal.
Login to save your score, XP, coins and progress.
What is the common ratio of the sequence \(81,27,9,3,\ldots\)?
B. \(\frac{1}{3}\)
सार्व अनुपात \(\frac{27}{81}=\frac{1}{3}\) है। घटती गुणोत्तर श्रेढ़ी में अनुपात (1) से छोटा हो सकता है। / The common ratio is \(\frac{27}{81}=\frac{1}{3}\). In a decreasing geometric progression the ratio can be less than (1).
Login to save your score, XP, coins and progress.
If \(a_n=2\cdot4^{n-1}\), what is the value of \(a_5\)?
C. (512)
\(a_5=2\cdot4^4=512\)। घात में (n-1) का मान पहले निकालें। / \(a_5=2\cdot4^4=512\). First find the value of (n-1) in the exponent.
Login to save your score, XP, coins and progress.
In the geometric progression \(7,14,28,56,\ldots\), which term is (224)?
C. (6)वाँ(6)th
पद (7,14,28,56,112,224) हैं, इसलिए (224) छठा पद है। छोटे प्रश्नों में पद लिखकर जांचना तेज है। / The terms are (7,14,28,56,112,224), so (224) is the sixth term. For small questions listing terms is quick.
Login to save your score, XP, coins and progress.
Which sequence is not a geometric progression?
C. \(2,4,8,15,\ldots\)
\(2,4,8,15,\ldots\) में अनुपात \(2,2,\frac{15}{8}\) बराबर नहीं हैं। गुणोत्तर श्रेढ़ी में अनुपात स्थिर होना चाहिए। / In \(2,4,8,15,\ldots\), the ratios \(2,2,\frac{15}{8}\) are not equal. A geometric progression must have a constant ratio.
Login to save your score, XP, coins and progress.
If a geometric progression has (a=6) and (r=2), what are the first four terms?
B. (6,12,24,48)
पहला पद (6) है और हर बार (2) से गुणा करने पर (6,12,24,48) मिलते हैं। गुणोत्तर श्रेढ़ी में अगला पद गुणा करके बनता है। / The first term is (6), and multiplying by (2) each time gives (6,12,24,48). In a geometric progression each next term is formed by multiplication.
Login to save your score, XP, coins and progress.
What is the common ratio of the sequence \(2,-6,18,-54,\ldots\)?
B. (-3)
सार्व अनुपात \(\frac{-6}{2}=-3\) है। ऋणात्मक अनुपात होने पर चिह्न बारी-बारी से बदलते हैं। / The common ratio is \(\frac{-6}{2}=-3\). With a negative ratio the signs alternate.
Login to save your score, XP, coins and progress.
What is the next term in the geometric progression \(4,12,36,\ldots\)?
D. (108)
सार्व अनुपात (3) है, इसलिए अगला पद \(36\cdot3=108\) होगा। अगले पद के लिए पिछले पद को अनुपात से गुणा करें। / The common ratio is (3), so the next term is \(36\cdot3=108\). Multiply the previous term by the ratio for the next term.
Login to save your score, XP, coins and progress.
If (3,x,27) are three consecutive positive terms of a geometric progression, what is (x)?
B. (9)
मध्य पद (x) के लिए \(x^2=3\cdot27=81\), इसलिए (x=9)। धनात्मक पदों में ज्यामितीय माध्य धनात्मक लें। / For the middle term (x), \(x^2=3\cdot27=81\), so (x=9). For positive terms take the positive geometric mean.
Login to save your score, XP, coins and progress.
What is the sum of the first (4) terms of the geometric progression \(5,15,45,135,\ldots\)?
C. (200)
योग (5+15+45+135=200) है। कम पद हों तो सीधे जोड़ना सुरक्षित है। / The sum is (5+15+45+135=200). For a small number of terms direct addition is safe.
Login to save your score, XP, coins and progress.
If a geometric progression has \(a_2=10\) and (r=2), what is \(a_1\)?
B. (5)
\(a_2=a_1r\), इसलिए \(10=a_1\cdot2\) और \(a_1=5\)। पीछे जाने के लिए अनुपात से भाग दें। / \(a_2=a_1r\), so \(10=a_1\cdot2\) and \(a_1=5\). Divide by the ratio to move backward.
Login to save your score, XP, coins and progress.
If a geometric progression has \(a_1=4\) and \(a_4=108\), what is the common ratio?
B. (3)
\(a_4=a_1r^3\), इसलिए \(108=4r^3\) और \(r^3=27\), अतः (r=3)। पद-संख्या के अंतर को घात बनाएं। / \(a_4=a_1r^3\), so \(108=4r^3\) and \(r^3=27\), hence (r=3). Use the position gap as the exponent.
Login to save your score, XP, coins and progress.
What is the (6)th term of the sequence \(\frac{1}{2},1,2,4,\ldots\)?
B. (16)
सार्व अनुपात (2) है और पद \(\frac{1}{2},1,2,4,8,16\) हैं। क्रम से गुणा करते जाएं। / The common ratio is (2), and the terms are \(\frac{1}{2},1,2,4,8,16\). Keep multiplying in order.
Login to save your score, XP, coins and progress.
What is the fifth term of the geometric progression \(64,32,16,8,\ldots\)?
B. (4)
सार्व अनुपात \(\frac{1}{2}\) है, इसलिए पाँचवाँ पद (4) है। घटती गुणोत्तर श्रेढ़ी में बार-बार अनुपात से गुणा करें। / The common ratio is \(\frac{1}{2}\), so the fifth term is (4). In a decreasing geometric progression multiply by the ratio repeatedly.
Login to save your score, XP, coins and progress.
If (a=3) and (r=5), what is \(a_4\)?
C. (375)
\(a_4=3\cdot5^3=375\)। (n)वें पद में घात (n-1) होती है। / \(a_4=3\cdot5^3=375\). In the (n)th term the exponent is (n-1).
Login to save your score, XP, coins and progress.
Which option has common ratio \(\frac{1}{4}\)?
B. \(64,16,4,1,\ldots\)
\(64,16,4,1,\ldots\) में \(\frac{16}{64}=\frac{1}{4}\) है। अनुपात के लिए लगातार पदों को भाग दें। / In \(64,16,4,1,\ldots\), \(\frac{16}{64}=\frac{1}{4}\). Divide consecutive terms to find the ratio.
Login to save your score, XP, coins and progress.
In the geometric progression \(1,3,9,27,\ldots\), which term is (81)?
B. (5)वाँ(5)th
पद (1,3,9,27,81) हैं, इसलिए (81) पाँचवाँ पद है। घातों को क्रम से पहचानें। / The terms are (1,3,9,27,81), so (81) is the fifth term. Identify powers in order.
Login to save your score, XP, coins and progress.
If \(a_n=9\left(\frac{1}{3}\right)^{n-1}\), what is \(a_3\)?
A. (1)
\(a_3=9\left(\frac{1}{3}\right)^2=1\)। भिन्न अनुपात में घात की गणना सावधानी से करें। / \(a_3=9\left(\frac{1}{3}\right)^2=1\). Calculate powers of fractional ratios carefully.
Login to save your score, XP, coins and progress.
If (2,6,x,54) is a geometric progression, what is (x)?
B. (18)
सार्व अनुपात \(\frac{6}{2}=3\) है, इसलिए \(x=6\cdot3=18\)। समान अनुपात को हर अगले पद पर लगाएं। / The common ratio is \(\frac{6}{2}=3\), so \(x=6\cdot3=18\). Apply the same ratio to each next term.
Login to save your score, XP, coins and progress.
Which sequence has a negative common ratio?
C. \(5,-10,20,-40,\ldots\)
\(5,-10,20,-40,\ldots\) में सार्व अनुपात (-2) है। ऋणात्मक अनुपात से पदों के चिह्न बदलते हैं। / In \(5,-10,20,-40,\ldots\), the common ratio is (-2). A negative ratio changes the signs of terms.
Login to save your score, XP, coins and progress.
What is the sum of the first (4) terms of the geometric progression \(10,20,40,80,\ldots\)?
B. (150)
योग (10+20+40+80=150) है। कम पद हों तो सीधे जोड़ना आसान है। / The sum is (10+20+40+80=150). For a small number of terms direct addition is easy.
Login to save your score, XP, coins and progress.
If a geometric progression has \(a_3=20\) and (r=2), what is \(a_1\)?
B. (5)
\(a_3=a_1r^2\), इसलिए \(20=a_1\cdot4\) और \(a_1=5\)। दो पद पीछे जाने के लिए \(r^2\) से भाग दें। / \(a_3=a_1r^2\), so \(20=a_1\cdot4\) and \(a_1=5\). Divide by \(r^2\) to move two terms backward.
Login to save your score, XP, coins and progress.
What is the (n)th term of the sequence \(6,18,54,162,\ldots\)?
A. \(a_n=6\cdot3^{n-1}\)
पहला पद (6) और अनुपात (3) है, इसलिए \(a_n=6\cdot3^{n-1}\)। सामान्य पद में पहला पद और अनुपात दोनों रखें। / The first term is (6) and the ratio is (3), so \(a_n=6\cdot3^{n-1}\). Use both first term and ratio in the general term.
Login to save your score, XP, coins and progress.
If (a=1) and (r=2), what will be the sum of the first (6) terms?
B. (63)
पहले (6) पद (1,2,4,8,16,32) हैं और योग (63) है। (2) की घातों के योग को ध्यान से जोड़ें। / The first (6) terms are (1,2,4,8,16,32), and their sum is (63). Add powers of (2) carefully.
Login to save your score, XP, coins and progress.
If \(a_1=12\) and \(r=\frac{1}{2}\), what is \(a_4\)?
A. \(\frac{3}{2}\)
(a_4=12\left\(\frac{1}{2}\right\)3=\frac{3}{2})। भिन्न अनुपात में हर बार आधा होता है। / (a_4=12\left\(\frac{1}{2}\right\)3=\frac{3}{2}). With a fractional ratio each term becomes half.
Login to save your score, XP, coins and progress.
Which value of (x) makes (4,20,x) a geometric progression?
C. (100)
सार्व अनुपात \(\frac{20}{4}=5\) है, इसलिए \(x=20\cdot5=100\)। तीसरे पद के लिए दूसरे पद को अनुपात से गुणा करें। / The common ratio is \(\frac{20}{4}=5\), so \(x=20\cdot5=100\). Multiply the second term by the ratio to get the third term.
Login to save your score, XP, coins and progress.
In the sequence \(2,8,32,128,\ldots\), which term is (512)?
B. (5)वाँ(5)th
सार्व अनुपात (4) है और पद (2,8,32,128,512) हैं। पद-संख्या के लिए क्रम से पद बनाएं। / The common ratio is (4), and the terms are (2,8,32,128,512). For position form terms in order.
Login to save your score, XP, coins and progress.
If a geometric progression has \(a_2=18\) and \(a_4=162\), what is (r)?
B. (3)
\(a_4=a_2r^2\), इसलिए \(162=18r^2\) और \(r^2=9\), धनात्मक अनुपात (r=3) है। पदों के बीच दूरी को घात बनाएं। / \(a_4=a_2r^2\), so \(162=18r^2\) and \(r^2=9\), giving positive ratio (r=3). Use the gap between terms as the exponent.
Login to save your score, XP, coins and progress.
What is the fifth term of the geometric progression \(1,-2,4,-8,\ldots\)?
B. (16)
सार्व अनुपात (-2) है, इसलिए पाँचवाँ पद ((-8)(-2)=16) है। ऋणात्मक अनुपात में चिह्न बदलता है। / The common ratio is (-2), so the fifth term is ((-8)(-2)=16). With a negative ratio signs alternate.
Login to save your score, XP, coins and progress.
Which option has the first four terms of a geometric progression with (a=9) and (r=3)?
C. (9,27,81,243)
पहला पद (9) है और हर बार (3) से गुणा करने पर (9,27,81,243) मिलते हैं। (a) और (r) दोनों को मिलाएं। / The first term is (9), and multiplying by (3) each time gives (9,27,81,243). Match both (a) and (r).
Login to save your score, XP, coins and progress.
If \(5,15,45,\ldots\) is a geometric progression, what is the product of the first three terms?
A. (3375)
गुणनफल \(5\cdot15\cdot45=3375\) है। गुणनफल में हर पद को सावधानी से गुणा करें। / The product is \(5\cdot15\cdot45=3375\). Multiply each term carefully in product questions.
Login to save your score, XP, coins and progress.
What is the next term in the geometric progression \(100,50,25,\ldots\)?
B. \(\frac{25}{2}\)
सार्व अनुपात \(\frac{1}{2}\) है, इसलिए अगला पद \(25\cdot\frac{1}{2}=\frac{25}{2}\) होगा। अनुपात से गुणा करें। / The common ratio is \(\frac{1}{2}\), so the next term is \(25\cdot\frac{1}{2}=\frac{25}{2}\). Multiply by the ratio.
Login to save your score, XP, coins and progress.
If \(a_n=4\cdot2^{n-1}\), which sequence does it form?
C. \(4,8,16,32,\ldots\)
(n=1,2,3,4) रखने पर (4,8,16,32) मिलते हैं। नियम से शुरू के पद बनाकर विकल्प मिलाएं। / Putting (n=1,2,3,4) gives (4,8,16,32). Form the initial terms from the rule and match the option.
Login to save your score, XP, coins and progress.
If (x,12,36) are consecutive terms of a geometric progression, what is (x)?
C. (4)
\(\frac{36}{12}=3\), इसलिए \(\frac{12}{x}=3\) और (x=4)। लगातार अनुपात बराबर रखें। / \(\frac{36}{12}=3\), so \(\frac{12}{x}=3\) and (x=4). Keep consecutive ratios equal.
Login to save your score, XP, coins and progress.
What is the (6)th term of the geometric progression \(8,24,72,\ldots\)?
C. (1944)
यहाँ (r=3), इसलिए \(a_6=8\cdot3^5=1944\)। (6)वें पद में (5) बार अनुपात लगता है। / Here (r=3), so \(a_6=8\cdot3^5=1944\). The sixth term uses the ratio (5) times.
Login to save your score, XP, coins and progress.
Which sequence has common ratio (5)?
B. \(2,10,50,250,\ldots\)
\(2,10,50,250,\ldots\) में हर बार (5) से गुणा हो रहा है। अनुपात के लिए अगले पद को पिछले पद से भाग दें। / In \(2,10,50,250,\ldots\), each term is multiplied by (5). For the ratio divide the next term by the previous term.
Login to save your score, XP, coins and progress.
If \(a_1= \frac{3}{4}\) and (r=2), what is \(a_4\)?
C. (6)
\(a_4=\frac{3}{4}\cdot2^3=6\)। भिन्न पहले पद के साथ घात को सावधानी से गुणा करें। / \(a_4=\frac{3}{4}\cdot2^3=6\). Multiply the power carefully with the fractional first term.
Login to save your score, XP, coins and progress.
What is the sum of the first (5) terms of the geometric progression \(2,4,8,16,\ldots\)?
C. (62)
पहले (5) पद (2,4,8,16,32) हैं और योग (62) है। पदों को क्रम से लिखकर जोड़ें। / The first (5) terms are (2,4,8,16,32), and the sum is (62). Write the terms in order and add.
Login to save your score, XP, coins and progress.
If \(a_1=3\) and (r=-2), what are the first four terms?
B. (3,-6,12,-24)
हर बार (-2) से गुणा करने पर (3,-6,12,-24) मिलते हैं। ऋणात्मक अनुपात से चिह्न बदलते हैं। / Multiplying by (-2) each time gives (3,-6,12,-24). A negative ratio makes the signs alternate.
Login to save your score, XP, coins and progress.
For which (x) will (8,x,18) be consecutive terms of a positive geometric progression?
B. (12)
\(x^2=8\cdot18=144\), इसलिए धनात्मक (x=12)। मध्य पद ज्यामितीय माध्य होता है। / \(x^2=8\cdot18=144\), so positive (x=12). The middle term is the geometric mean.
Login to save your score, XP, coins and progress.
What is the (n)th term of the sequence \(7,21,63,189,\ldots\)?
A. \(a_n=7\cdot3^{n-1}\)
पहला पद (7) और अनुपात (3) है, इसलिए \(a_n=7\cdot3^{n-1}\)। सामान्य पद में पहला पद और अनुपात रखें। / The first term is (7) and the ratio is (3), so \(a_n=7\cdot3^{n-1}\). Use the first term and ratio in the general term.
Login to save your score, XP, coins and progress.
If \(a_2=24\) and \(a_5=192\), and the ratio is positive, what is (r)?
A. (2)
\(a_5=a_2r^3\), इसलिए \(192=24r^3\) और \(r^3=8\), अतः (r=2)। पदों की दूरी घात तय करती है। / \(a_5=a_2r^3\), so \(192=24r^3\) and \(r^3=8\), hence (r=2). The gap between positions decides the exponent.
Login to save your score, XP, coins and progress.
In the geometric progression \(3,12,48,\ldots\), what is \(a_5\)?
C. (768)
सार्व अनुपात (4) है, इसलिए \(a_5=3\cdot4^4=768\)। (5)वें पद के लिए (4) बार अनुपात लगता है। / The common ratio is (4), so \(a_5=3\cdot4^4=768\). For the fifth term the ratio is used (4) times.
Login to save your score, XP, coins and progress.
If a geometric progression has \(a_1=2\) and \(a_3=50\), what is the positive (r)?
C. (5)
\(a_3=a_1r^2\), इसलिए \(50=2r^2\) और \(r^2=25\), अतः धनात्मक (r=5)। धनात्मक अनुपात मांगने पर धनात्मक मूल लें। / \(a_3=a_1r^2\), so \(50=2r^2\) and \(r^2=25\), hence positive (r=5). When positive ratio is asked take the positive root.
Login to save your score, XP, coins and progress.
Which statement is correct for \(12,6,3,\frac{3}{2},\ldots\)?
B. यह \(r=\frac{1}{2}\) वाली गुणोत्तर श्रेढ़ी हैIt is a geometric progression with \(r=\frac{1}{2}\)
हर पद पिछले पद का आधा है, इसलिए \(r=\frac{1}{2}\) है। अनुपात जांचने के लिए अगला पद पिछले पद से भाग दें। / Each term is half of the previous term, so \(r=\frac{1}{2}\). To check the ratio divide the next term by the previous term.
Login to save your score, XP, coins and progress.
If \(a_n=256\) in \(1,4,16,64,\ldots\), what is (n)?
B. (5)
पद (1,4,16,64,256) हैं, इसलिए (n=5)। पद-संख्या के लिए क्रम से घात पहचानें। / The terms are (1,4,16,64,256), so (n=5). For position identify powers in order.
Login to save your score, XP, coins and progress.
In the geometric progression \(2,6,18,54,\ldots\), what is \(a_3+a_4\)?
C. (72)
\(a_3=18\) और \(a_4=54\), इसलिए योग (72) है। दोनों पद अलग निकालकर जोड़ें। / \(a_3=18\) and \(a_4=54\), so the sum is (72). Find both terms separately and then add.
Login to save your score, XP, coins and progress.
C. (30)
पहले चार पद (16,8,4,2) हैं और योग (30) है। घटती गुणोत्तर श्रेढ़ी में पद क्रम से लिखें। / The first four terms are (16,8,4,2), and the sum is (30). In a decreasing geometric progression write the terms in order.
Login to save your score, XP, coins and progress.
This level is designed for 50 active questions. Currently 50 questions are available for the selected class and difficulty.
Yes, the timer uses 35 seconds per question for Medium difficulty and shows the total remaining time on the page.
Yes, every question has its own SEO-friendly page with answer, explanation and related practice links.
Use Google login or mobile OTP. Admin can block users and control login providers.