Sequence And Series Question 440
Question: If the sum of $ n $ terms of an A.P. is $ 2n^{2}+5n $ , then the $ n^{th} $ term will be
[RPET 1992]
Options:
A) $ 4n+3 $
B) $ 4n+5 $
C) $ 4n+6 $
D) $ 4n+7 $
Show Answer
Answer:
Correct Answer: A
Solution:
Given that $ S_{n}=2n^{2}+5n $ Putting $ n=1,\ 2,\ 3,\ ……….,\ S_1=2\times 1+5\times 1=7\ $ , $ S_2=2\times 4+10=8+10=18,\ S_3=18+15=33 $ . So, $ T_1=S_1=a=7,\ T_2=S_2-S_1=18-7=11 $ , $ T_3=S_3-S_2=33-18=15 $ Therefore series is $ 7,,11,\ 15,,…….. $ Now, $ n^{th} $ term $ =a+(n-1)d=7+(n-1)4=4n+3 $ . Aliter: As we know $ T_{n}=S_{n}-{S_{n-1}} $ $ =(2n^{2}+5n)-{ 2,{{(n-1)}^{2}}+5,(n-1) } $ $ =2n^{2}+5n-2n^{2}+4n-2-5n+5=4n+3 $ .
BETA
