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Find the number of terms

Posted March 31st, 2008 by alpha
in

How many terms of the AP(arithmetic progression):9,17,25,............... must be taken to give a sum of 636?

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Answer

On April 9th, 2008 Structure says:

Sum of arithmetic progression is

$$s_n=n\frac{a_1+a_n}{2}=n\frac{a_1+a_1+(n-1)r}{2}=n\frac{2a_1+(n-1)r}{2}$$

In your problem $ a_1=9;\:r=8;\:s_n=636 $
so you have to solve equation

$$n\frac{18+(n-1)8)}{2}=636=12*53$$

or

$$n(9+4(n-1))=12*53$$
$$n(4n+5)=12(4*12+5)$$

so

$$n=12$$

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