Question

What is the sum of the arithmetic sequence 153, 139, 125, …, if there are 22 terms?

Answer 1

`6600`

Explanation:

First, find the value of `a`. The value of `a` is the first term in the sequence you've been given. This progression does not succeed, it reduces with every term.

Therefore, `a=153`

Then find the difference between the values you have been given. Knowing that this is an arithmetic sequence, the difference `d` between the values should be equal. You can find this by subtracting the first and second value away from each other like so:

`153-139=14`
`139-125=14`

Therefore, `d=14`

We also have been told that there are `22` terms. This is the value of the `nth` term.

`n=22`

Now the sum of all the terms in the arithmetic sequence can be found by substituting in the values for `n`, `d` and `a`:

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

`Sn = (22/2)((2*153)+(22-1)*14)`

`Sn = 11(306+294)`

`Sn = 6600`