Question

the sum of the first seven terms of an AP is 63 and sum of the next seven terms is 161. Find the 28th term​

Answer 1

e S7 = 63. Also given sum of its next 7 terms is 161. But Sum of first 14 terms = sum of first 7 terms + sum of next 7 terms.

Answer 2

Answer:

Sum of n terms of an A.P. = n/2 (2 a + (n-1)d)

where a is the 1st term of A.P and d is the common difference

So,sum of 1st 7 terms=7/2 (2 a + 6d)=63

2a+6d = 18 —(equation 1)

Sum of next 7 terms=

sum of 1st 14 terms- sum of 1st 7 terms =

14/2 (2 a + 13d) - 7/2 (2 a + 6d)

So, 161 = 14a +91d - 63

224 =14 a +91d—(equation 2)

(Eq. 1 )*7 - (eq. 2)

14 a + 42d- 14a - 91d =126-224

49d = 98

d = 2,a = 3

Nth term = a +(n-1)d

28th term = 3 + 27×2 = 57

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