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If the first term of AP is 4 and the sum of first five term is equal to one-fourth of the sum of the next five term, then find the 15th term?​

 Dec 26, 2021
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The first term of an arithmetic progression is  4.

The common difference is  d.

 

The fifth term is  4 + 4d.

 

The sum of the first five terms is:  Sum  =  5[ 4 + (4 + 4d) ] / 2  =  20 + 10d

 

The sixth term is  4 + 5d

The tenth term is  4 + 9d

 

The sum of the next five terms is:  Sum  =  5[ (4 + 5d) + (4 + 9d) ] / 2  =  20 + 35d

 

Since the sum of the first five terms is one-fourth the sum of the next five terms:

              20 + 10d  =  ¼( 20 + 35d)

 

Solving:  d  =  -12,'

 

Since you know the first term and the common difference, you can find the 15th term.

 Dec 26, 2021

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