A) 3925
B) 4100
C) 4175
D) 8200
Correct Answer: C
Solution :
[c] As given. \[{{n}^{th}}\]term is : \[{{T}_{n}}=3n+7\] Sum of n term, \[{{S}_{n}}=\sum{{{T}_{n}}}\] \[=\sum{(3n+7)=3\sum{n+7}\sum{1}}\] \[=\frac{3n(n+1)}{2}+7n=n\left[ \frac{3n+3+14}{2} \right]\] \[=n\left[ \frac{3n+17}{2} \right]\] Sum of 50 terms \[={{S}_{50}}=50\left[ \frac{3\times 50+17}{2} \right]\] \[=50\left[ \frac{167}{2} \right]=25\times 167=4175\]
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