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  • The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

Q : 18     The sum of the  \small 4th and  \small 8th terms of an AP is  \small 24 and the sum of the \small 6th and \small 10th terms is \small 44  Find the first three terms of the AP.
 

Answers (1)

best_answer

It is given that
sum of the  \small 4th and  \small 8th terms of an AP is  \small 24 and the sum of the \small 6th and \small 10th terms is \small 44
i.e.
a_4+a_8=24
\Rightarrow a+3d+a+7d=24
\Rightarrow 2a+10d=24
\Rightarrow a+5d=12 \ \ \ \ \ \ \ \ \ \ \ \ \ -(i)
And
a_6+a_{10}=44
\Rightarrow a+5d+a+9d=44
\Rightarrow 2a+14d=44
\Rightarrow a+7d=22 \ \ \ \ \ \ \ \ \ \ \ \ \ -(ii)
On solving equation (i) and (ii) we will get 
a= -13 \ and \ d= 5
Therefore,first three of AP with a = -13 and d = 5 is
-13,-8,-3
 

Posted by

Gautam harsolia

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