SOLUTION: The second and fifth terms of an arithmetic sequence are 17 and 19, respectively. What is the eighth term?

Question 1038745: The second and fifth terms of an arithmetic sequence are 17 and 19, respectively. What is the eighth term?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A2 = 17
A5 = 19
A5 - A2 = 2
5 - 2 = 3
average difference is 2/3.
since this is an arithmetic sequence, it has to be the common difference.

the formula for an arithmetic sequence is An = A1 + (n-1)*d
An is the nth term.
A1 is the first term.
d is the common difference.

A2 is therefore equal to A1 + 1 * 2/3 because 2 minus 1 is equal to 1 and the common difference is equal to 2/3.
since A2 is equal to 17, you get 17 = A1 + 2/3.
solve for A1 to get A1 = 16 and 1/3.

using the same formula, if A1 is correct and d is correct, A5 should be equal to 16 and 1/3 + 4*2/3 which would make it equal to 16 and 1/3 + 8/3 which would make it equal to 16 and 9/3 which makes it equal to 16 and 3 which make it equal to 19.

looks like the formula works and the common difference is 2/3 and the first term is 16 and 1/3.

the eighth term would be A8.
based on the formula A8 = 16 and 1/3 + 7*2/3 which becomes A8 = 16 and 1/3 + 14/3 which becomes A8 = 16 and 15/3 which becomes A8 = 16 and 5 which makes A8 equal to 21.

start with A5 = 19
add 2/3 to get A6 = 19 and 2/3.
add 2/3 to get A7 = 20 and 1/3.
add 2/3 to get A8 = 21.

everything checks out ok so the solution looks good.

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