SOLUTION: If the first term of the arithmetic sequence is 5 and the ninth term is 29, where would the number 101 be found?

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Question 739888: If the first term of the arithmetic sequence is 5 and the ninth term is 29, where would the number 101 be found?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Basic Expression for Term of the Sequence (arithmetic):
5%2B%28n-1%29d
n is the index of the term
d is the common difference between terms

Given for n=9, term is 29.
5%2B%289-1%29d=29
5%2B8d=29
8d=29-5
8d=24
d=3

More Specific Formula for Expression of each Term:
5%2B%28n-1%29%2A3

The number, 101 will have an expression for this value :
5%2B%28n-1%29%2A3=101
FIND n.
5%2B3n-3=101
3n%2B2=101
3n=99
n=99%2F3
highlight%28n=33%29.