Question

17 times the 17th term of an A.P. is equal to 18 times the 18th term. Find the 35th term of this progression.

Answer 1

Given:

17 × T₁₇​ = 18 × T_18​

We have to find the 35th term, i.e., T₃₅.

T_n​ = a + (n − 1)d

T₁₇​ = a + 16d

T₁₈​ = a + 17d

Substitute in the given condition

17(a + 16d) = 18(a + 17d)

17a + 272d = 18a + 306d

17a − 18a = 306d − 272d

−a = 34d

⇒ a = −34d

T₃₅ ​= a + 34d

T_35​ = −34d + 34d

T_35​ = 0