Sequence And Series Question 73
Question: If $ S_1,\ S_2,\ S_3,………..S_{m} $ are the sums of $ n $ terms of $ m $ A.P.’s whose first terms are $ 1,\ 2,\ 3,\ ……………,m $ and common differences are $ 1,\ 3,\ 5,\ ………..2m-1 $ respectively, then $ S_1+S_2+S_3+…….S_{m}= $
Options:
A) $ \frac{1}{2}mn(mn+1) $
B) $ mn(m+1) $
C) $ \frac{1}{4}mn(mn-1) $
D) None of the above
Show Answer
Answer:
Correct Answer: A
Solution:
Here $ a=1,\ 2,\ 3,,……..,m;\ \ \ d=1,\ 3,\ 5,……..,2m-1 $ and $ n=n $ , then $ S_1+S_2+…….+S_{m}=\frac{1}{2}mn(mn+1) $ $ [ Using\ S\ =\frac{m}{2}(a+l).\ Since\ S_1,\ S_2,\ S_3,……S_{m}\ form\ an\ A\text{.P}\text{.} ] $
BETA
