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)15.

Explanation:

We know that a_7 = 3a7=3 and a_16 = -15a16=15.

We also know that a_n = a_1 + (n-1)dan=a1+(n1)d.

a_16 = a_1 + (16-1)da16=a1+(161)d

Equation (1): -15 = a_1 + 15d15=a1+15d

and

a_7 = a_1 + (7-1)da7=a1+(71)d

Equation (2): 3 = a_1 + 6d3=a1+6d

Subtract Equation (2) from Equation (1).

-15-3 = 15d-6d153=15d6d

-18 = 9d18=9d

d = -18/9d=189

Equation (3): d= -2d=2

Substitute Equation (3) in Equation (1).

-15 = a_1 + 15d15=a1+15d

-15 = a_1 + 15(-2) = a_1 -3015=a1+15(2)=a130

a_1 = 30-15a1=3015

a_1 = 15a1=15