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 15.

Explanation:

We know that a7=3 and a16=15.

We also know that an=a1+(n1)d.

a16=a1+(161)d

Equation (1): 15=a1+15d

and

a7=a1+(71)d

Equation (2): 3=a1+6d

Subtract Equation (2) from Equation (1).

153=15d6d

18=9d

d=189

Equation (3): d=2

Substitute Equation (3) in Equation (1).

15=a1+15d

15=a1+15(2)=a130

a1=3015

a1=15