Question

The 5^th term and the 9^th term of an Arithmetic Progression are 4 and – 12 respectively.

Find:

1. the first term
2. common difference
3. sum of 16 terms of the AP.

Answer 1

Let a and d be the first term and common difference of A.P.

Then by T_n = a + (n – 1)d

Given T₅ = 4

`\implies` a + 4d = 4   ...(1)

And T₉ = – 12

`\implies` a + 8d = – 12   ...(2)

Solving equations (1) and (2), we get

– 4d = 16

`\implies` d = – 4

Put this value in equation (1)

a + 4 × (– 4) = 4

a – 16 = 4

a = 20

∴ a. First term a = 20

b. Common difference d = – 4

c. Sum of n terms = `n/2 [2a + (n - 1)d` 

∴ Sum of 16 terms = `16/2 [2 xx 20 + 15 xx (-4)]`

= 8 [40 – 60]

= 8 × (– 20)

= – 160