SOLUTION: The sum of first 20 and 50 terms of an AP is 420 and 2550. Find the eleventh term of a GP whose first term is the same as the AP and the common ratio is equal tithe common differen

Algebra ->  Sequences-and-series -> SOLUTION: The sum of first 20 and 50 terms of an AP is 420 and 2550. Find the eleventh term of a GP whose first term is the same as the AP and the common ratio is equal tithe common differen      Log On


   



Question 891695: The sum of first 20 and 50 terms of an AP is 420 and 2550. Find the eleventh term of a GP whose first term is the same as the AP and the common ratio is equal tithe common difference of the AP ?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the first n terms of an AP is given by
A%5Bn%5D+=+%28n%2F2%29%2A%282%2Aa%5B1%5D+%2B+%28n-1%29d%29
==> A%5B20%5D+=+10%282%2Aa%5B1%5D+%2B+19d%29+=+420+
and A%5B50%5D+=+25%282%2Aa%5B1%5D+%2B+49d%29+=+2550
or 2%2Aa%5B1%5D+%2B+19d+=+42+ and 2%2Aa%5B1%5D+%2B+49d+=+102+
Solving these equations give
a%5B1%5D+=+d+=+2
==> g%5B11%5D+=+g%5B1%5D%2Ar%5E%2811-1%29+=+2%2A2%5E10+=+2%5E11+=+2048