SOLUTION: An = -3, 2,7,12,17,…. a- Determine a138 b- Determine the first 40 terms of an

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Question 933368: An = -3, 2,7,12,17,….
a- Determine a138
b- Determine the first 40 terms of an

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If a%5B1%5D=-3 , a%5B2%5D=2 , a%5B3%5D=7 , a%5B4%5D=12 , a%5B5%5D=17 ,
and so on, following the presumed pattern where a%5Bn%5D=5%2Ba%5Bn-1%5D ,
this is an arithmetic sequence,
with first term a%5B1%5D=-3 , and common difference d=5 .
For an arithmetic sequence,
term number {{n}}} is a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad ,
and the sum of the first n terms is S%5Bn%5D=%28n%2F2%29%282a%5B1%5D%2B%28n-1%29%2Ad%29 .
So,
a%5B138%5D=-3%2B%28138-1%29%2A5=-3%2B137%2A5=-3%2B685=highlight%28682%29
and .