SOLUTION: given a term in an arithmetic sequence and the common difference, find the 52nd term and the explicit formula http://prntscr.com/scu0c8

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Question 1158458: given a term in an arithmetic sequence and the common difference, find the 52nd term and the explicit formula
http://prntscr.com/scu0c8

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

13.
an Arithmetic Sequence as a rule:
a%5Bn%5D+=+a%5B1%5D+%2B+d%28n-1%29
a%5B32%5D=622+->n=32 if d=20
622+=+a%5B1%5D+%2B+20%2832-1%29
622+=+a%5B1%5D+%2B+20%2831%29
622+=+a%5B1%5D+%2B+620
+a%5B1%5D=+622-+620
+a%5B1%5D=+2
the explicit formula is:
a%5Bn%5D+=+2+%2B+20%28n-1%29
the 52nd term is:
a%5B52%5D+=+2+%2B+20%2852-1%29
a%5B52%5D+=+2+%2B+20%2851%29
a%5B52%5D+=+2+%2B+1020
a%5B52%5D+=+1022

14.
a%5Bn%5D+=+a%5B1%5D+%2B+d%28n-1%29
a%5B18%5D=-166+->n=18 if d=-8
-166=+a%5B1%5D+-8%2818-1%29
-166=+a%5B1%5D+-8%2817%29
-166=+a%5B1%5D+-136
136-166=+a%5B1%5D+
a%5B1%5D+=-30
the explicit formula is:
a%5Bn%5D+=+-30+-8%28n-1%29

the 52nd term is:
a%5B52%5D+=+-30+-8%2852-1%29
a%5B52%5D+=+-30+-8%2851%29
a%5B52%5D+=+-30+-408
a%5B52%5D+=++-438