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?

Guest Dec 26, 2021

#1**+1 **

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.

geno3141 Dec 26, 2021