If the fifth term of a ap is 19 and the tenth term is 34 find: - a) the first term b) the common difference c) the sum of the first 15 term

a) The first term is a=7

b) The common difference is d=3

c) The sum of the first 15 term is 420.    

Step-by-step explanation:

Given : If the fifth term of a AP is 19 and the tenth term is 34.

To find : a) the first term b) The common difference c) The sum of the first 15 term ?

Solution :

The Arithmetic progression is in the form,

Where, a is the first term and d is the common difference

The nth term of the A.P is

The fifth term of a AP is 19.

...(1)

The tenth term is 34.

...(2)

Solving (1) and (2) by subtracting the equations,

Substitute in (1),

a) The first term is a=7

b) The common difference is d=3

c) The sum of the first 15 term is given by,

The sum of the first 15 term is 420.

the monthly balance will be $75,000