SOLUTION: The first two terms of an arithmetic sequnce are 3, 7 and the last term is 355. a. How many terms are there? b. What is the 40th term? c. What is the sum of the series?

Algebra ->  Sequences-and-series -> SOLUTION: The first two terms of an arithmetic sequnce are 3, 7 and the last term is 355. a. How many terms are there? b. What is the 40th term? c. What is the sum of the series?       Log On


   

Question 1047684: The first two terms of an arithmetic sequnce are 3, 7 and the last term is 355.
a. How many terms are there?
b. What is the 40th term?
c. What is the sum of the series?
Thanks in advance for helping out! I understand the concept but am having difficulty in solving this problem.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
The first two terms of an arithmetic sequence are 3, 7 and the last term is 355.
Thanks in advance for helping out! I understand the concept but am having difficulty in solving this problem.
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First of all, the common difference is 4. 

a. How many terms are there?  - How many intervals of the length of 4 are there between 3 and 355? %28355-3%29%2F4%29 = 352%2F4 = 88.

                              - How many terms are there in between including endpoints? 88+1 = 89.


b. What is the 40th term?     - It is easy, and if you understand the concept, you must answer it. 
                                a%5B40%5D = a%5B1%5D+%2B+%28n-1%29%2Ad = 3 +39*4 = calculate on your own.

c. What is the sum of the series?    S%5Bn%5D = %28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An = %28%283+%2B+355%29%2F2%29%2A89 = calculate it on your own


There is a bunch of lessons on arithmetic progression in this site.
The introductory level lessons are
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Solved problems on arithmetic progressions


Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Note the description is Arithmetic Progression, and you are given first two terms, meaning these are the two CONSECUTIVE terms. 7-3=4, common difference. General term of the sequence, 3%2B%28n-1%29%2A4=highlight%283%2B4%28n-1%29%29.

(a) and (b) should be very simple now.
(c) ? If you know how many terms in the sequence, call this v, then %28v%2F2%29%28firstTerm%2BlastTerm%29 is the sum of the finite sequence.