Question

Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?

Hence find the sum of all the terms of the Arithmetic Progression (A.P.)

Answer 1

Given A.P. is 15, 30, 45, 60.........

Here a = 15, d = 30 – 15 = 15

Let T_n = 300

T_n  = a + (n – 1)d

300 = 15 + (n – 1) × 15

300 = 15 + 15n – 15

15n = 300

∴ n = 20

Hence, 300 is the 20^th term

Also by S_n = `n/2 [2a + (n - 1)d]`

S₂₀ = `20/2 [2 xx 15 + (20 - 1) xx 15]`

= 10[30 + 285]

= 10 × 315

∴ S₂₀ = 3150