The sum of how many terms of the series 6 + 12 + 18 + 24 + … is 1800 ?

Question: The sum of how many terms of the series 6 + 12 + 18 + 24 + … is 1800 ?
[A].

16

[B].

24

[C].

20

[D].

18

Answer: Option B

Explanation:

This is an A.P. in which a = 6, d = 6 and Sn = 1800

Then,	n	[2a + (n – 1)d] = 1800
	2

	n	[2 x 6 + (n – 1) x 6] = 1800
	2

3n (n + 1) = 1800

n(n + 1) = 600

n2 + n – 600 = 0

n2 + 25n – 24n – 600 = 0

n(n + 25) – 24(n + 25) = 0

(n + 25)(n – 24) = 0

n = 24

Number of terms = 24.