Question

Find the value of x if 3 + 6 + 9 + ... + 96 = x.

Answer 1

a = 3

d = 6 − 3

= 3

a_n = 96

a_n = a + (n − 1)d

96 = 3 + (n − 1)3

96 − 3 = (n − 1)3

93 = (n − 1)3

`93/3 = n − 1`

31 + 1 = n

n = 32

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

= `32/2[2(3) + (32 - 1)3]`

= 16[6 + 31 × 3]

= 16[6 + 93]

= 16 × 99

= 1,584