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Q.

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of the AP.


Class: 10


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a

50

b

57

c

64

d

69                                                                                                                                                                                                                            

answer is B.

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Detailed Solution

Sum of first n terms of an
Given: S­7 = 63
2a + 6d = 18   …(1)
Also, sum of next 7 terms is 161.
Thus, Sum of first 14 terms = Sum of first.
7 terms + Sum of next 7 terms.
S14 = 63 + 161 = 224
2a + 13d = 32   …(2)
Solving eq (1) & (2), we get,
a = 3 and d = 2
Therefore,
T28 = a + (28 – 1)d
 T28 = 3 + 27 × 2
T28 = 3 + 54 = 57
  
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The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of the AP.Class: 10