Question

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

Answer 1

Answer: -216

Step-by-step explanation:

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

$Sn=\frac{(a_1+a_n)n}{2}$

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:

$S_{24}=\frac{(152-170)(24)}{2}=-216$

Answer 2

Answer:

Sn = -216

Step-by-step 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:

$S_n =\frac{n(a_1+a_n)}{2}$

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:

$S_n =\frac{24(152-170)}{2}$

$S_n=-216$