Verified Answer :

I needed my brother to help me with this one,so here is the answer.
The common difference is -14. 

Let's simplify this by expressing each term as 
163 - 14n 
where n is the number of the term. 

Then the sum of the 28 terms is 
28 163 - 14 (1+2+3+...+28) 
= 4,564 - 14 28 * 29 / 2 
= -1,120 

The sum of the arithmetic sequence is -1120.

What is arithmetic sequence?

"It is a sequence of numbers in which the difference between consecutive terms is constant."

What is the sum of arithmetic sequence?

"\(S_n=\frac{n}{2}[2a +(n-1)d]\)

where a as the first term,

d the common difference between the consecutive terms,

n is the total number of terms in the sequence."

For given question,

We have been given an arithmetic sequence  149, 135, 121,. . .

The first term of given arithmetic sequence is 149

⇒ a = 149

The common difference is,

⇒ d = 135 - 149

⇒ d = -14

There are 28 terms.

⇒ n = 28

Using the formula for  the sum of an arithmetic sequence,

\(\Rightarrow S=\frac{n}{2}[2a +(n-1)d]\\\\\Rightarrow S=\frac{28}{2}[2\times (149) +(28-1)\times (-14)]\\\\\Rightarrow S=14\times[298-378]\\\\\Rightarrow S=14\times (-80)\\\\\Rightarrow S=-1120\)

Therefore, the sum of the arithmetic sequence is -1120.

Learn more about the arithmetic sequence here:

https://brainly.com/question/25749583

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