Question
Thu February 26, 2009 By:

Arithmetic Progression

Expert Reply
Fri February 27, 2009

Let the first term be a and the common difference be d.

Remember that two find two unknown quantities, we must have two equations involving them, which we'll solve and get the answer.

the first seven terms are

a,a+d, a+2d...a+6d

So their sum= (7/2)[a+a+6d]=(7/2)[2a+6d]

So,

 according to question

(7/2)[2a+6d]=20

This gives us

7a+21d=20...(i)

The next seven terms are

a+7d,a+8d,...a+13d

these terms can be thought of as in A.P. with first terms as a+7d and common difference as d.

 

So their sum =  (7/2)[a+7d+a+13d]=17

This gives us

7a+70d=17..(ii)

Solving the two equations we get

the values of a and d.

 

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