Question

the sum of the first 7 terms of an ap is 63 and the sum of its next 7 term is 161 find the 28 term of the AP

Answer 1

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Here your solution
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The first n terms of an A.P, Sn
= ( n / 2) [ 2a + ( n -1)d ]

Given that sum of the first 7 terms of an A.P is 63 i. e S7
= 63.

= ( 7 / 2) [ 2a + 6d ] = 63

= 2a + 6d = 18 --------(1)

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.

S14 = 63 + 161 = 224

= ( 14 / 2) [ 2a + 13d ] = 224
= 7 [ 2a + 13d ] = 224.

= [ 2a + 13d ]
= 32 -------92)

SOLVING EQUATION
(1) and (2)

d = 2 and a = 3.

Now
t28 = a + ( 28 - 1) d

t28 = 3 + ( 28 - 1) 2

t28 = 57.

= 28th term of this A.P. is
57.


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