Sequence And Series Question 418
Question: If the nth term of an arithmetic progression is $ 3n+7 $ , then what is the sum of its first 50 terms?
Options:
A) 3925
B) 4100
C) 4175
D) 8200
Show Answer
Answer:
Correct Answer: C
Solution:
[c] As given. $ n^{th} $ term is : $ T_{n}=3n+7 $ Sum of n term, $ S_{n}=\sum{T_{n}} $ $ =\sum{(3n+7)=3\sum{n+7}\sum{1}} $ $ =\frac{3n(n+1)}{2}+7n=n[ \frac{3n+3+14}{2} ] $ $ =n[ \frac{3n+17}{2} ] $ Sum of 50 terms $ =S_{50}=50[ \frac{3\times 50+17}{2} ] $ $ =50[ \frac{167}{2} ]=25\times 167=4175 $
BETA
