Hello, rpatel!

The sum of the first six terms of an artithmetic series is 21.

The seventh term is three times the sum of the third and fourth.

Find the first term and the common difference.

You are expected to know these formulas: ( = first term, = common difference)

The term: .

The sum of the first terms: .

We are told that sum of the first six terms is 21: .

. . which simplifies to: .[1]

The term is:

The term is:

The term is:

We are told: the term is 3 times the sum of the and

Hence, we have: .

. . which simplifies to: .[2]

Solve the system of equations: . .(Use your favorite method)

And get: .