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?
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.