Hello, me2612!

]The first term of an arithmetic series is 9

and the seventh term is three times the second term.

a) Find the sum of the first 32 terms.

We are told: .

In general: .

We have: .

Then: .

Formula: .

Therefore: .

The sum of terms is 5040:b) How many more terms must be added for the sum of the A.P. to be 5040?

. .

This factors: .

. . and has the positive root: .

The sum of the first 32 terms is 3264.

The sum of the first 40 terms is 5040.

Therefore: . more terms must be added.