Question

The sum of first 7 terms of ap is 63 and sum of next 7 terms is 161 find 28th term of ap

Answer 1

Solution:-

Sum of the n terms of an AP = Sn = n/2{2a + (n - 1)d}
S₇ = 63
63 = 7/2{2a(7 - 1)d}
126 = 14a + 42d
Dividing it by 2, we get
2a + 6d = 18 ...........(1)

Now,
Sum of first 14 terms = sum of first 7 terms and sum of next 7 terms
S₁₄ = 63 + 161
S₁₄ = 224
⇒ 224 = 14/2{2a(14 - 1)d}
⇒ 448 = 28a + 182d
⇒ Dividing it by 7, we get
⇒ 2a + 13d = 32 ...............(2)
Subtracting (1) from (2), we get
7d = 14
d = 2
Substituting the value of d =2 in (1), we get
2a + 6*2 = 18
⇒ 2a + 12 = 18
⇒ 2a = 18 - 12
⇒ 2a = 6
⇒ a = 3
Now, 
a₂₈ = a + (n - 1)d
= 3 + (28 - 1)2
= 3 + 27*2
= 3 + 54
a₂₈ = 57
So, 28th term is 57. 
Answer.