Question

Find the sum.
14 + 42 + 70 + ... + (28n − 14)

Answer 1

14n^2.

Explanation:

This is Arithmetic with first term a = 14 and common difference d = 28.

Sum of n terms = n/2[2a + (n-1)d]

= n/2(28 +( n -1)28]

= n/2(28 + 28n - 28)

= 14n^2

Answer 2

14n²

Explanation:

14 = 14 *1

42 = 14 *3

70 = 14 *5

28n -14 = 14*2n - 14 = 14*(2n -1)

14 + 42 + 70 + ........+(28n -14) = 14*1 + 14*3 + 14*5 + ....... + 14*(2n - 1)

= 14 * (1 + 3 + 5 + ......+ (2n-1) )

= 14 * n²

= 14n²

1 + 3 + 5 + .... +(2n -1) -> sum of first 'n' odd numbers.

Formula for finding sum of first 'n' odd numbers = n²