Question

How many terms are there in the AP 6, 10, 14, 18, ..., 174?

Answer 1

In the given AP, a = 6 and d = (10 – 6) = 4

Suppose that there are n terms in the given AP.

Then, `T_n = 174`

⇒ a + (n – 1) d = 174

⇒ 6 + (n – 1) × 4 = 174

⇒ 2 + 4n = 174 

⇒ 4n = 172

⇒ n = 43
Hence, there are 43 terms in the given AP.