Question

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

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Here,

Given,

S(7) = 63

As we know that,

S(n) = n/2[2a + (n - 1)d]

So,

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

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

Also,

Sum of 14 terms,

S(14) = S(1st 7) + S(Another 7)

= 63 + 161

= 224

So,

14/2[2a + 13d] = 32 ...............(2)

Now,

Subtract (1) & (2),

(2a + 13d) - (2a + 6d) = 32 - 18

7d = 14

d = 14/7

d = 2

Now,

Substitute the value of d in (1),

2a + 6d = 18

2a + 6(2) = 18

2a + 12 = 18

2a = 18 - 12

2a = 6

a = 6/2

a = 3

As we know that,

a(n) = a + (n - 1)d

a(28) = 3 + 2 × (27)

a(28) = 57

Therefore,

28th term of the AP = 57