The 9th and the 12th term of an arithmetic progression are 50 and 65 respectively find the sum of the first 70 terms

Sum of the first 70 terms is 12,775

Step-by-step explanation:

For the 9th term, the formula is;

a + 8d = 50

For the 12th

a + 11d = 65

Subtract this from the equation above;

3d = 15

d = 15/3 = 5

To get a, we have a + 8(5) = 50

a = 10

The 70th term

will be

a + 69d

= 10 + 69(5)

= 355

Sum of the first 70

= n/2(a + L)

= 70/2( 10 + 355)

= 35 * 365 = 12,775