Question

How many terms are there in the AP 6,1 0, 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.