Why is important to note that the formula only applies to Arithmetic Progressions (AP), where the common difference is constant. Which of find the based on the assumption that the common difference is constant.

Prove to which is the definition of an arithmetic progression.

Class 10th Maths NCERT Books for CBSE Board and state Board.

# Find the number of terms in each of the following APs : 18, 15(1/2), 13, . . . , – 47

Share

Here, a = 18 and d = 15(1/2) – 18 = – 5/2.

Let, the total number of terms in the A.P. is n.

Therefore, a_n = – 47

⇒ a + (n – 1)d = – 47

⇒ 18 + (n – 1)(- 5/2) = – 47

⇒ (n – 1)(- 5/2) = – 65

⇒ n – 1 = 26

⇒ n = 27

Hence, there are 27 terms in the given A.P.