Sequence And Series Question 146
Question: The sum of few terms of any ratio series is 728, if common ratio is 3 and last term is 486, then first term of series will be
[UPSEAT 1999]
Options:
A) 2
B) 1
C) 3
D) 4
Show Answer
Answer:
Correct Answer: A
Solution:
$ \therefore n^{th} $ term of series $ =a{r^{n-1}} $ $ =a,{{(3)}^{n-1}}=486 $ ?..(i) and sum of n terms of series. $ S_{n}=\frac{a(3^{n}-1)}{3-1} $ $ =728,(\because ,r>1) $ ?..(ii) From (i), $ a( \frac{3^{n}}{3} )=486 $ or $ a{{.3}^{n}}=3\times 486=1458 $ From (ii), $ a{{.3}^{n}}-a=728\times 2 $ or $ a{{.3}^{n}}-a=1456 $ $ 1458-a=1456 $
Þ $ a=2 $ .
BETA
