What is the first term of an arithmetic sequence in which the seventh term is 3 and the sixteenth term is -15?

1 Answer
Jul 17, 2015

The first term of the sequence is color(red)(15).

Explanation:

We know that a_7 = 3 and a_16 = -15.

We also know that a_n = a_1 + (n-1)d.

a_16 = a_1 + (16-1)d

Equation (1): -15 = a_1 + 15d

and

a_7 = a_1 + (7-1)d

Equation (2): 3 = a_1 + 6d

Subtract Equation (2) from Equation (1).

-15-3 = 15d-6d

-18 = 9d

d = -18/9

Equation (3): d= -2

Substitute Equation (3) in Equation (1).

-15 = a_1 + 15d

-15 = a_1 + 15(-2) = a_1 -30

a_1 = 30-15

a_1 = 15