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

Question

Philoid · Accepted Answer

In the given AP, the first term = a = 6

Common difference = d = 10 - 6 = 4

Last term = 174

To find: No. of terms in the AP.

Since, we know that

a_n = a + (n - 1) × d

∴ 174 = 6 + (n - 1) × 4

⇒ 174 - 6 = 4n - 4

⇒ 168 = 4n - 4

⇒ 168 + 4= 4n

⇒ 4n = 172

⇒ n = 172/4

⇒ n = 43

∴ Number of terms = 43.