Question

the first term of an arithmetic sequence is 10 and the sum of the first five terms is 250,find the sequence​

Answer 1

The sequence is:

10, 30, 50, 70, 90.....................

Explanation:

We have,

First term (a) = 10

Common difference (d) = ?

Sum of first 5 terms (
`S_(5)`) = 250

or,
`(n)/(2) [{2a+(n-1)d}] = 250`

or,
`(5)/(2) [2*10 + 4d]=250`

or,
`(5)/(2) * 4[5+d]=250`

or, 10(5 + d) =250

or, 5 + d = 25

∴ d = 20

Now,

2nd term = a + d = 10 + 20 = 30

3rd term = a + 2d = 10 + 2*20 = 10 + 40 = 50

4th term = a + 3d = 10 + 3*20 = 10 + 60 = 70

5th term = a + 4d = 10 + 4*20 = 10 + 80 = 90