SOLUTION: The fourth term of an arithmetic sequence is 17, and the sixth term is 11. Find the second term.

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Question 1141346: The fourth term of an arithmetic sequence is 17, and the sixth term is 11. Find the second term.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28A%2Bd%284-1%29=17%2CA%2Bd%286-1%29=11%29


system%28A%2B3d=17%2CA%2B5d=11%29

2d=-6

highlight%28d=-3%29


If you start at the fourth term and move downward by 2d, then.....

OR, 26-3=highlight%2823%29----------------the second term of the progression

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by the other tutor is a good formal mathematical solution; you should know how to find the answer by that method.

If you just need the answer quickly and don't need to be formal, use logical reasoning.

(1) If the sequence is arithmetic, then the second, fourth, and sixth terms form an arithmetic sequence.
(2) Since the 4th term is 6 more than the 6th, the 2nd term is 6 more than the 4th.
ANSWER: The second term is 17+6 = 23.