If the (11)th term of an AP is (52) and (d=5), what is (a_2)?
Correct answer: A
(a_2=a_{11}-9d=52-45=7). When moving backward from a known term, subtract the position gap times (d).
View question detailsMathematics
Finding the $n$th term of an AP
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Medium · Level 64 · ap,known-term,backward,class10
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- (7)
- (12)
- (17)
- (22)
Medium · Level 64 · ap,word-problem,nth-term,class10
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- (40) cm
- (43) cm
- (46) cm
- (49) cm
Medium · Level 64 · ap,word-problem,savings,nth-term
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- (₹850)
- (₹900)
- (₹950)
- (₹1000)
Medium · Level 64 · arithmetic progression,nth term,ap word problem,seating arrangement,class 10 mathematics
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- 54
- 56
- 58
- 60
Medium · Level 64 · arithmetic progression,nth term,word problem,decimal,sequence formula
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- 66.5 cm
- 68.5 cm
- 70 cm
- 71.5 cm
Medium · Level 64 · ap,word-problem,decreasing,nth-term
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- (240)
- (260)
- (280)
- (300)
Medium · Level 64 · arithmetic progression,nth term,common difference,class 10 mathematics,sequence
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- 76
- 80
- 84
- 88
Medium · Level 64 · ap,direct-formula,difference-of-terms,class10
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- (45)
- (54)
- (63)
- (72)
Medium · Level 64 · arithmetic progression,first term,nth term,common difference,class 10 mathematics
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- 0
- 5
- 10
- 15
Medium · Level 64 · arithmetic progression,nth term,common difference,algebra,class 10 mathematics
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- 10
- 12
- 14
- 16
Medium · Level 64 · ap,negative-term,term-number,class10
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- (18)
- (19)
- (20)
- (21)
Medium · Level 64 · ap,two-terms,nth-term,class10
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- (92)
- (94)
- (97)
- (99)
Medium · Level 64 · arithmetic progression,nth term,common difference,fractions,class 10 mathematics
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- 20
- 21
- 22
- 23
Medium · Level 64 · arithmetic progression,nth term,linear sequence,class 10 mathematics,term number
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- 13th term
- 14th term
- 15th term
- 16th term
Medium · Level 64 · ap,two-terms,backward,class10
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- (17)
- (19)
- (21)
- (23)
Medium · Level 64 · arithmetic progression,nth term,term number,linear equations,class 10 mathematics
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- 11
- 12
- 13
- 14
Medium · Level 64 · ap,symbolic,nth-term,class10
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- (0)
- (p+q)
- (p-q)
- (q-p)
Medium · Level 64 · arithmetic progression,nth term,common difference,class 10 mathematics,ap terms
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- 0
- -1
- 1
- 3
Medium · Level 64 · ap,multiples,nth-term,class10
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- (441)
- (448)
- (455)
- (462)
Medium · Level 64 · ap,multiples,less-than,nth-term
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- (189)
- (196)
- (198)
- (199)
In a staircase, the first step height is (10) cm and each next step is (3) cm higher. What is the height of the (12)th step?
Correct answer: B
This is an AP with (a=10), (d=3). (a_{12}=10+11\times3=43) cm. In word problems, identify the first term and difference.
View question detailsIn a savings plan, (₹200) is deposited in the first week and (₹50) more is deposited each week. What is the deposit in the (15)th week?
Correct answer: B
(a=200), (d=50), so (a_{15}=200+14\times50=900). The weekly deposit is the term, not the total amount.
View question detailsA theatre has (18) seats in the first row and each next row has (2) more seats. How many seats are in the (20)th row?
Correct answer: B
This forms an arithmetic progression with first term \(a=18\), common difference \(d=2\), and \(n=20\). Using \(a_n=a+(n-1)d\), \(a_{20}=18+(20-1)\times2=18+38=56\). Therefore, the 20th row has 56 seats. Choosing 58 would result from incorrectly adding the difference one extra time. Exam tip: in the \(n\)th term, the common difference is added \(n-1\) times.
View question detailsA plant is (25) cm tall on the first day and grows (1.5) cm daily. What will be its height on the (30)th day?
Correct answer: B
This is an arithmetic progression with first term \(a=25\) cm and common difference \(d=1.5\) cm. The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{30}=25+(30-1)\times1.5=25+43.5=68.5\) cm. Hence, 68.5 cm is correct. The value 70 cm can result from incorrectly adding \(30\times1.5\); the plant grows only 29 times after the first day. Exam tip: use \((n-1)d\), not \(nd\), for the \(n\)th term of an AP.
View question detailsA machine makes (500) items in the first hour and production decreases by (20) items each next hour. What is the production in the (14)th hour?
Correct answer: A
Here (a=500), (d=-20), so (a_{14}=500+13(-20)=240). In decreasing word problems, take (d) as negative.
View question detailsThe number of pages in chapters of a book increases as (12,16,20,\ldots). How many pages will the (18)th chapter have?
Correct answer: B
This is an arithmetic progression with first term \(a=12\) and common difference \(d=16-12=4\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{18}=12+(18-1)\times4=12+68=80\). Hence, the 18th chapter will have 80 pages. Option 84 would result from incorrectly using a larger increase than the actual common difference. Exam tip: Always use \(n-1\), not \(n\), in the nth-term formula.
View question detailsIf the (n)th term of an AP is (a_n=9n+2), what is the value of (a_{11}-a_5)?
Correct answer: B
(a_{11}-a_5=(101)-(47)=54), or (6d=6\times9=54). Use the difference of positions for term differences.
View question detailsIn an AP, (a_{15}=70) and (a_{25}=120). What is (a_1)?
Correct answer: A
In an AP, the difference between two terms equals the corresponding number of common differences. Thus, \(a_{25}-a_{15}=10d\), so \(120-70=10d\) and \(d=5\). Now, using \(a_{15}=a_1+14d\), we get \(70=a_1+14\times5\), hence \(a_1=0\). Option 5 is the common difference, not the first term. Exam tip: In \(a_n=a_1+(n-1)d\), remember to use \(n-1\).
View question detailsIf the (10)th term of the AP (x, x+4, x+8,\ldots) is (50), what is the value of (x)?
Correct answer: C
Here, the first term is \(a=x\) and the common difference is \(d=4\). Using \(a_n=a+(n-1)d\), we get \(50=x+(10-1)\times4=x+36\). Hence, \(x=14\). If 16 were chosen, the 10th term would be \(16+36=52\), not 50. Exam tip: In the nth-term formula, use \(n-1\), not \(n\).
View question detailsThe (n)th term of the AP (27,24,21,\ldots) is (-30). What is (n)?
Correct answer: C
From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
View question detailsIf (a_7=29) and (a_{14}=64), what is the value of (a_{21})?
Correct answer: D
(d=\frac{64-29}{14-7}=5), hence (a_{21}=64+7\times5=99). Equal position gap (7) gives term gap (35).
View question detailsIn an AP, \(a=4\) and \(d=\frac{3}{2}\). What is \(a_{13}\)?
Correct answer: C
The \(n\)th term of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{13}=4+(13-1)\times\frac{3}{2}=4+12\times\frac{3}{2}=4+18=22\). Hence, 22 is correct. Getting 21 would mean the common difference has not been multiplied correctly. Exam tip: always use \((n-1)\), not \(n\), in the formula for \(a_n\).
View question detailsIf (a_n=50-4n), which term of the AP will be (-10)?
Correct answer: C
Given \(a_n=50-4n\). For the term whose value is \(-10\), set \(50-4n=-10\). Thus, \(4n=60\), so \(n=15\). Therefore, \(-10\) is the 15th term of the AP. The 14th term is \(50-4(14)=-6\), so it is not correct. Exam tip: To find a term number, equate the given term value to \(a_n\) and solve for \(n\).
View question detailsIn an AP, (a_{10}=31) and (a_{18}=55). What is (a_6)?
Correct answer: B
(d=\frac{55-31}{8}=3), so (a_6=31-4\times3=19). When moving backward from a known term, subtract (d).
View question detailsIn the AP (8,14,20,\ldots), (a_n=74). Find the value of (n).
Correct answer: B
The first term is 8 and the common difference is 6. Using \(a_n=a+(n-1)d\), \(74=8+(n-1)\times6\). Thus, \(66=6(n-1)\), so \(n-1=11\) and \(n=12\). If \(n=13\), the term would be \(8+12\times6=80\), not 74. Exam tip: after finding \(n-1\), remember to add 1 to obtain the term number.
View question detailsIf the (p)th term of an AP is (q) and the (q)th term is (p), what is its ((p+q))th term?
Correct answer: A
Subtracting the relations gives (d=-1), and substitution gives (a_{p+q}=0). Even in symbolic APs, use (a_n=a+(n-1)d).
View question detailsIf the (3)rd term of an AP is (8) and the (8)th term is (3), what is the (11)th term?
Correct answer: A
Given \(a_3=8\) and \(a_8=3\), we have \(a_8-a_3=5d\). Thus, \(3-8=5d\), so \(d=-1\). Now \(a_{11}=a_8+3d=3+3(-1)=0\). Hence, 0 is the correct answer. Option 1 is the value of \(a_{10}\), obtained by counting one term less. Exam tip: When using two known terms of an AP, take the difference of their term numbers to find the number of common differences.
View question detailsThe first three-digit number is (100), which is not divisible by (7), but (105,112,119,\ldots) is the AP of three-digit multiples of (7). What is the (50)th term of this AP?
Correct answer: B
In this AP, (a=105), (d=7), so (a_{50}=105+49\times7=448). In an AP of multiples, choose the first correct multiple.
View question detailsWhat is the last term among the positive multiples of (9) less than (200)?
Correct answer: C
In (9,18,27,\ldots), (9n<200), so the greatest (n=22) and the term is (198). For multiples, take the largest integer below the limit.
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