Question

What is the sum of the arithmetic sequence 140, 136, 132…, if there are 35 terms?

2,520

2,590

2,660

2,930

Answer 1

what formula would i use here @Dr.V ?

Answer 2

Ok, a bit harder question. You must first find the 35th term to use the formula from the previous problem. The explicit definition for this arithmetic sequence is 140 -4(n-1). Substitute n = 35 to find the 35th term in the sequence, then use the formula for the sum of a finite arithmetic series.

Answer 3

Thanks!

Answer 4

My pleasure. Sequences and series are great stuff !

Answer 5

wait, what do i do after i get the -122? what would it be equivalent to?

Answer 6

where would i place it in the next formula?

Answer 7

How did you get -122?

Answer 8

i did 14-4(35-1)

Answer 9

or would it be 340?

Answer 10

Ooops! You should do 140-4(n-1). 140 is the first term in the sequence.

Answer 11

oh wow, haha, i didnt notice that

Answer 12

It is easy to make typos!

Answer 13

i got 4

Answer 14

Great! Now try subbing into the formula we used for the other problem. Type in your substitution.

Answer 15

I don´t think i can do it since the wording is different :/

Answer 16

The summation formula is
\[\frac{ n(first term + last term) }{ 2}\]

Answer 17

what would go in the (n) field? would the 4 be the last term?

Answer 18

n=35?

Answer 19

n is the number of terms in the sum. You are correct--4 is the last term