SOLUTION: the 5th term of a sequence is -17 and the 11th term is -47. construct an arithmetic sequence that would model this pattern

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Question 963684: the 5th term of a sequence is -17 and the 11th term is -47. construct an arithmetic sequence that would model this pattern
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Basic Term in General for Arithmetic Sequence:
A%5Bn%5D=A%5B1%5D%2B%28n-1%29d
A[n], general n term
A[1], first term
n, index of the term
d, common difference to each successive term


Let a be the first term of the sequence, d understood as already said;

system%28-17=a%2B%285-1%29d%2C-47=a%2B%2811-1%29d%29

system%28a%2B4d=-17%2Ca%2B10d=-47%29

Subtract corresponding equation members:
6d=17-47
6d=-30

highlight%28d=-5%29

You also want to know "a". Use either equation from the system.
a=-17-4d
a=-17-4%28-5%29
-17%2B20
highlight%28a=3%29

You can find the first few terms of the sequence......!