Question

What is the sum of the sequence 152,138,124, ... if there are 24 terms?

Answer 1

Sn = -216

Explanation:

We are given the following sequence and we are to find the sum of the given sequence if there are 24 terms in it:

`152, 138, 124, ...`

We know that the formula of sum for an arithmetic sequence is given by:

`S_n =(n(a_1+a_n))/(2)`

where
`a_1` is the first term (124)and
`a_n` is the last term
`a_(24)`.

To find
`a_1`, we will use the following formual:

`a_n=a_1+(n-1)d`

`a_24=152+(24-1)(-14)`

`a_(24)=170`

Substituting the given values in the above formula to get the sum:

`S_n =(24(152-170))/(2)`

`S_n=-216`

Answer 2

Answer: -216

Explanation:

To solve the exercise you must use the formula shown below:

`Sn=((a_1+a_n)n)/(2)`

Where:

`a_1=152\\a_n=a_(24)`

You should find
`a_(24)`

The formula to find it is:

`a_n=a_1+(n-1)d`

Where d is the difference between two consecutive terms.

`d=138-152=-14`

Then:

`a_(24)=152+(24-1)(14)=-170`

Substitute it into the first formula. Therefore, you obtain:

`S_(24)=((152-170)(24))/(2)=-216`