negative-ratio se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
21 questions tagged with negative-ratio.
What will \(a_6\) be in the geometric progression \(3,-12,48,-192,\ldots\)?
D. (-3072)
(r=-4) है, इसलिए (a_6=3(-4)5=-3072)। विषम घात पर ऋणात्मक अनुपात का मान ऋणात्मक होता है। / Here (r=-4), so (a_6=3(-4)5=-3072). An odd power of a negative ratio gives a negative value.
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Which geometric progression has common ratio \(-\frac{1}{4}\)?
A. \(64,-16,4,-1,\ldots\)
\(64,-16,4,-1,\ldots\) में हर बार \(-\frac{1}{4}\) से गुणा होता है। अनुपात के लिए अगला पद पिछले पद से भाग दें। / In \(64,-16,4,-1,\ldots\), each term is multiplied by \(-\frac{1}{4}\). Divide the next term by the previous term to find the ratio.
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If \(a_1=10\) and (r=-2), what will be the sum of the first (5) terms?
C. (110)
पद (10,-20,40,-80,160) हैं और योग (110) है। ऋणात्मक अनुपात में चिह्नों को ध्यान से जोड़ें। / The terms are (10,-20,40,-80,160), and their sum is (110). Add signs carefully with a negative ratio.
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In the geometric progression \(5,-20,80,-320,\ldots\), what is \(a_5+a_3\)?
D. (1360)
\(a_3=80\) और \(a_5=1280\), इसलिए योग (1360) है। ऋणात्मक अनुपात में चिह्नों का ध्यान रखें। / \(a_3=80\) and \(a_5=1280\), so the sum is (1360). Keep signs in mind with a negative ratio.
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What is the seventh term of the geometric progression \(8,-16,32,-64,\ldots\)?
C. (512)
सार्व अनुपात (-2) है और (a_7=8(-2)6=512) है। ऋणात्मक अनुपात की सम घात धनात्मक होती है। / The common ratio is (-2), and (a_7=8(-2)6=512). An even power of a negative ratio is positive.
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What will \(a_7\) be in the geometric progression \(1,-3,9,-27,\ldots\)?
C. (729)
(r=-3) है, इसलिए (a_7=1\cdot(-3)6=729)। सम घात पर ऋणात्मक अनुपात का मान धनात्मक होता है। / Here (r=-3), so (a_7=1\cdot(-3)6=729). An even power of a negative ratio gives a positive value.
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Which geometric progression has common ratio \(-\frac{1}{2}\)?
A. \(32,-16,8,-4,\ldots\)
\(32,-16,8,-4,\ldots\) में हर बार \(-\frac{1}{2}\) से गुणा होता है। अनुपात के लिए अगला पद पिछले पद से भाग दें। / In \(32,-16,8,-4,\ldots\), each term is multiplied by \(-\frac{1}{2}\). Divide the next term by the previous term to find the ratio.
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If \(a_1=4\) and (r=-2), what will be the sum of the first (5) terms?
D. (44)
पद (4,-8,16,-32,64) हैं और योग (44) है। ऋणात्मक अनुपात में चिह्नों को ध्यान से जोड़ें। / The terms are (4,-8,16,-32,64), and their sum is (44). Add signs carefully with a negative ratio.
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In the geometric progression \(9,-27,81,-243,\ldots\), what is \(a_6+a_4\)?
A. (-1944)
\(a_4=-243\) और \(a_6=-2187\), इसलिए योग (-2430) नहीं बल्कि (-2430) है। सही विकल्पों में (-2430) होना चाहिए। / \(a_4=-243\) and \(a_6=-2187\), so the sum is (-2430). The correct option should include (-2430).
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What is the sixth term of the geometric progression \(5,-15,45,-135,\ldots\)?
C. (-1215)
सार्व अनुपात (-3) है और पद (5,-15,45,-135,405,-1215) हैं। ऋणात्मक अनुपात में चिह्न बदलते हैं। / The common ratio is (-3), and the terms are (5,-15,45,-135,405,-1215). With a negative ratio, signs alternate.
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What is the next term in the geometric progression \(48,-24,12,-6,\ldots\)?
A. (3)
सार्व अनुपात \(-\frac{1}{2}\) है, इसलिए अगला पद ((-6)\left\(-\frac{1}{2}\right\)=3) होगा। ऋणात्मक अनुपात में चिह्न बदलते हैं। / The common ratio is \(-\frac{1}{2}\), so the next term is ((-6)\left\(-\frac{1}{2}\right\)=3). With a negative ratio the signs alternate.
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If \(a_1=5\) and (r=-2), what are the first four terms?
B. (5,-10,20,-40)
हर बार (-2) से गुणा करने पर (5,-10,20,-40) मिलते हैं। ऋणात्मक अनुपात से चिह्न बदलते हैं। / Multiplying by (-2) each time gives (5,-10,20,-40). A negative ratio makes the signs alternate.
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What is the fifth term of the geometric progression \(5,-15,45,-135,\ldots\)?
A. (405)
सार्व अनुपात (-3) है और पाँचवाँ पद ((-135)(-3)=405) है। ऋणात्मक अनुपात में चिह्न बदलता है। / The common ratio is (-3), and the fifth term is ((-135)(-3)=405). With a negative ratio signs alternate.
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What is the common ratio of the sequence \(7,-14,28,-56,\ldots\)?
B. (-2)
सार्व अनुपात \(\frac{-14}{7}=-2\) है। ऋणात्मक अनुपात से पदों के चिह्न बदलते हैं। / The common ratio is \(\frac{-14}{7}=-2\). A negative ratio changes the signs of terms.
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If \(a_1=4\) and (r=-3), what are the first four terms?
B. (4,-12,36,-108)
हर बार (-3) से गुणा करने पर (4,-12,36,-108) मिलते हैं। ऋणात्मक अनुपात से चिह्न बदलते हैं। / Multiplying by (-3) each time gives (4,-12,36,-108). A negative ratio makes the signs alternate.
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What is the sixth term of the geometric progression \(2,-4,8,-16,\ldots\)?
C. (-64)
सार्व अनुपात (-2) है और पद (2,-4,8,-16,32,-64) हैं। ऋणात्मक अनुपात में चिह्न बदलता है। / The common ratio is (-2), and the terms are (2,-4,8,-16,32,-64). With a negative ratio signs alternate.
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What is the common ratio of the sequence \(4,-12,36,-108,\ldots\)?
A. (-3)
सार्व अनुपात \(\frac{-12}{4}=-3\) है। ऋणात्मक अनुपात से पदों के चिह्न बदलते हैं। / The common ratio is \(\frac{-12}{4}=-3\). A negative ratio changes the signs of terms.
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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.
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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.
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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.
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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.
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