CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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
loader
B
10
loader
C
5
loader
D
5
loader

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
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image