Question

If the 10^th term of an A.P. is 52 and the 17^th term is 20 more than the 13^th term, find the A.P.

Answer 1

In the given AP, let the first term be a and the common difference be d.

Then, T_n = a + (n − 1)d ​

Now, we have:

T₁₀ = a + (10 − 1)d

⇒ a + 9d = 52 ...(1)

T₁₃ = a + (13 − 1)d = a + 12d ...(2)

T₁₇ = a + (17 − 1)d = a + 16d ...(3)

But, it is given that T₁₇ = 20 + T₁₃

i.e., a + 16d = 20 + a + 12d

⇒ 4d = 20

⇒ d = 5

On substituting d = 5 in (1), we get:

a + 9 ⨯ 5 = 52

⇒​ a = 7

Thus, a = 7 and d = 5

∴ The terms of the AP are 7, 12, 17, 22,...