Question

Find the sum of the first 30 terms of the equation below: an=4n+1

Answer 1

Let n = 30

We are actually looking for a_30.

a_30 = 4(30) + 1

a_30 = 120 + 1

a_30 = 121

Answer 2

1,890 is the sum of the first 30 terms of the equation .

Explanation:

`a_n=4n+1`

if , n = 1

`a_1=4* 1+1=5`

If, n = 2

`a_2=4* 2+1=9`

If, n = 3

`a_3=4* 3+1=13`

The arithmetic sequence comes out to be:

5, 9, 13........

a = 5

d =
`a_2=a_1=9-5=4`

The sum of first 30 terms is given by:

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

`S_(30)=(30)/(2)* (2* 5+(30-1)* 4)`

`S_(30)=1,890`

1,890 is the sum of the first 30 terms of the equation .