Question

Find the sum of the first 11 terms of the sequence -7,-4,-1, 2 ...

Answer 1

Answer:

A    The sum of the first 11 terms is 88

Step-by-step explanation:

Since -4 - (-7) = -1 - (-4) = 2 - (-1) = 3

Your sequence is an arithmetic sequence with a common difference of 3.

The formula for the sum of an arithmetic sequence is

$S = \frac{n(a_{1} + a_{n}) }{2}$  where $a_{1} = the first term, a_{n} = the last term, n = the number of terms to be added, and S = the sum$

In your case $a_{1} = -7$,  n = 11  and $a_{n} = a_{11}$

We know everything except the eleventh term.

So, we need to find the eleventh term or  $a_{11}$ = $a_{1}$ + (n - 1)d

                                                                     =  -7 + (11 - 1)3

                                                                     = -7 + 30 = 23

Now, S = $\frac{11(-7 + 23)}{2} = \frac{11(16)}{2} = 88$

The sum of the first 11 terms is 88