arithmetic progression

Question

the sum of the arithmetic progression 4, ... ,76 is 1920. Find the number of terms and the common difference.

Answer 1

Let the number of terms be represented by the variable, n and the common difference by variable, d.

First term, a = 4

Last term, L = 76

Sum of n terms, Sn = 1920

Sum of terms in an arithmetic progression, Sn = (n/2)*(a + L) = (n/2)*[2a + (n - 1)*d]

Using the first equation,

(n/2)*(4 + 76) = 1920

(n/2)*(80) = 1920

n/2 = 1920/80

n = (1920/80) * 2

n = 48

Check:

Sn = (n/2)*(a + L) = (48/2)*(4 + 76) = 24 * 80 = 1920