Question

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

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,...