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

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Answer 1 · 2015-07-17T22:16:33

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

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).

$-15 = a_1 + 15d$

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

$a_1 = 30-15$

$a_1 = 15$