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Q.

If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, then what is the AP?


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a

7, 12, 17, 22

b

10, 15, 20, 25 

c

6, 8, 10, 12

d

8, 13, 18, 23

answer is B.

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Detailed Solution

Given that the 10th term of an AP is 52 and 17th term is 20 more than its 13th term. Let first term is a and the common difference is d.
Formula used for nth term of A.P.:
t n =a+ n−1 d
Apply formula of n th term of AP in the first given condition.
t 10 =a+(10−1)d ⇒52=a+9d        -----(1) Applying formula of nthterm of AP in the second given condition.  t 17 =20+ t 13
Apply formula of n th term of AP and calculate 13th term:
∴ t 13 =a+(13−1)d ⇒ t 13 =a+12d     -----(3) Apply formula of n th term of AP and calculate 17th term:
∴ t 17 =a+(17−1)d ⇒ t 17 =a+16d       ------(4)
Putting the value of t 17 from equation (3) in equation (2):
∴a+16d=20+a+12d ⇒4d=20 ⇒d= 20 4 ⇒d=5 Putting the value of d in equation (1):
∴a+9×5=52 ⇒a+45=52 ⇒a=52−45 ⇒a=7
Putting the value of a and d in the general series:
∴(7),[7+5],[7+2×5],[7+3×5],…… ⇒(7),(12),(7+10),(7+15),…… ⇒ (7),(12),(17),(22),… Therefore, AP series is 7,12,17,22.
Hence, option (2) is correct.
 
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