Question

How do you find the 25th partial sum of the arithmetic sequence `2, 8, 14, 20,...`?

Answer 1

See below

Explanation:

Using the sum formula `S_n= n/2(a_1+a_n)`

To figure out the 25th partial sum, it is essential to know it is just the sum of the first 25 numbers of the sequence.

We already have `n=25`
and `a_1=2`

To figure out `a_n` for the formula above, which is `a_25` in this case, we must write a rule:

Just by looking at the sequence we know the common difference is `6`

To write an explicit arithmetic rule:
`a_n= a_1+d(n-1)`
`a_n= 2+6(n-1)`

To solve for the 25term:
`a_25= 2+6(25-1)`
`a_25= 146`

Now to find the sum:
`S_25= 25/2(2+146)= 1850`