Sequence And Series Question 19
Question: The sums of $ n $ terms of three A.P.’s whose first term is 1 and common differences are 1, 2, 3 are $ S_1,\ S_2,\ S_3 $ respectively. The true relation is
Options:
A) $ S_1+S_3=S_2 $
B) $ S_1+S_3=2S_2 $
C) $ S_1+S_2=2S_3 $
D) $ S_1+S_2=S_3 $
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ a_1=a_2=a_3=1 $ and $ d_1=1,\ d_2=2,\ d_3=3 $ . Therefore, $ S_1=\frac{n}{2}(n+1) $ ……(i) $ S_2=\frac{n}{2}[2n] $ ……(ii) $ S_3=\frac{n}{2}[3n-1] $ ……(iii) Adding (i) and (iii), $ S_1+S_3=\frac{n}{2}[(n+1)+(3n-1)]=2[ \frac{n}{2}(2n) ]=2S_2 $ Hence correct relation $ S_1+S_3=2S_2 $ .
BETA
