SOLUTION: The 4th term of an arithmetic sequence is 16.The 8th term is four times the 1st term. (a)find the general term T(n)of the sequence. (b)Find the smallest term which is greater tha

Algebra ->  Sequences-and-series -> SOLUTION: The 4th term of an arithmetic sequence is 16.The 8th term is four times the 1st term. (a)find the general term T(n)of the sequence. (b)Find the smallest term which is greater tha      Log On


   

Question 430428: The 4th term of an arithmetic sequence is 16.The 8th term is four times the 1st term.
(a)find the general term T(n)of the sequence.
(b)Find the smallest term which is greater than 500.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
(a) a%5B4%5D+=+a%5B1%5D+%2B+3d+=+16, and a%5B8%5D+=+a%5B1%5D+%2B+7d+=+4a%5B1%5D
<==> 3a%5B1%5D+=+7d
==> a%5B1%5D+=+%287d%29%2F3
==> %287d%29%2F3+%2B+3d+=+16
==> %2816d%29%2F3+=+16
==> d = 3
==> a%5B1%5D+=+%287%2A3%29%2F3+=+7
==> T(n) = 7 + (n-1)3 = 7 + 3n - 3 = 3n + 4

(b) We want 3n + 4 > 500, or n > 165.333..... Hence when n = 166, we get the smallest term greater than 500, which is 3*166 + 4 = 502.