Question

# Find the common difference of an AP. whose first term is $$100$$ and the sum of whose first six terms is five times the sum of the next six terms.

A
10
B
10
C
5
D
5

Solution

## The correct option is B $$-10$$Here $$a=100$$Let difference is $$d$$.$$\Rightarrow a_1+a_2+a_3+a_4+a_5+a_6=5(a_7+a_8+a_9+a_{10}+a_{11}+a_{12})$$So by the formula, $$S_n = \dfrac{n}{2} (a+l)$$, where $$a$$ &$$l$$ are the first and last term of an AP, we have$$6\left(\dfrac{a_1+a_6}{2} \right)=5\times 6\left(\dfrac{a_7+a_{12}}{2}\right)$$$$\Rightarrow a_1+a_6=5(a_7+a_{12})$$$$\Rightarrow a+a+5d=5(a+6d+a+11d)$$$$\Rightarrow 2a+5d=10a+85d$$$$\Rightarrow 80d=-8a$$$$\Rightarrow d=\dfrac{-a}{10}\Rightarrow \dfrac{-100}{10}\Rightarrow -10$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More