Question

If the 10^th term of an AP is 52 and 17^th term is 20 more than its 13^th 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

\(\Rightarrow\) 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

\(\Rightarrow\) 4d = 20

\(\Rightarrow\) d = 5

On substituting d = 5 in (1), we get:

a + 9 x 5 = 52

\(\Rightarrow\) a = 7

Thus, a = 7 and d = 5

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