Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12.
Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12.

Solutions:

Provided here that,

The Third term, a3 = 16

As we all know,

a +(3−1)d = 16

a+2d = 16 ………………………………………. (i)

It is known that, 7th term exceeds the 5th term by 12.

a7 − a5 = 12

[a+(7−1)d]−[+(5−1)d]= 12

(a+6d)−(a+4d) = 12

2d = 12

d = 6

From equation (i), we get,

a+2(6) = 16

a+12 = 16

a = 4

As a result, A.P. will be 4, 10, 16, 22,…