Question

How many terms are there in the A.P.?

(i) 7, 10, 13, ... 43.

(ii) -1, -\(\frac{5}{6}\), -\(\frac{2}{3}\), -\(\frac{1}{2}\),...., \(\frac{10}{3}\)

(iii) 7, 13, 19, ..... , 205

(iv) 18, 15\(\frac{1}{2}\), 13, .... , - 47

Answer 1

(i) 7, 10, 13, ... 43.

a = 7, d = 3

A_n = 43

a + (n – 1) d = 43

7 + (n – 1) 3 = 43

3n = 39

n = 13

Therefore, there are total 13 terms in the A.P.

(ii)  -1, -\(\frac{5}{6}\), -\(\frac{2}{3}\), -\(\frac{1}{2}\),...., \(\frac{10}{3}\)

n = 26

(iii) 7, 13, 19, ..... , 205

a = 7, d = 6

A_n = 205

a + (n – 1) d = 205

7 + (n – 1) 6 = 205

6n = 204

n = 34

(iv)  18, 15\(\frac{1}{2}\), 13, .... , - 47

n = 27