Question

In an arithmetic sequence, the first term is 8, the common difference is 3 and the last term is 68.

a How many terms are there in this sequence?
b Find the sum of all the terms of the sequence.

Answer 1

Answer: a. 21 terms

b. 798

Explanation:

a. 68-8=60 ==> difference between 1st and last term

60/3=20 ==> number of terms after the first term

20+1=21 terms ==> total number of terms

b. Find the mean of the terms first:

(68+8)/2= ==> the mean of all terms in a sequence is equal to the mean of the first and last term

76/2=38

38*21=798 ==> add the mean 21 times to get the total sum since there are 21 terms in the sequence.