Question

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

Answer 1

here it is the answer is 252

Answer 2

Step-by-step explanation:

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

Where  

a =1st term of A.P and  

d = 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+(28-1)2

= 3 + 27×2  

=3+54

= 57

The 28th of A.P is 57

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