Question:
How many terms are there in the AP 6, 10, 14, 18,...,174?
Solution:
In the given AP, a = 6 and d = (10 - 6) = 4
Suppose that there are n terms in the given AP.
Then Tn = 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.