Question

What is a1 of the arithmetic sequence for which a3=10 and a51=−182?

Answer 1

Answer:

a₁ = 18

Step-by-step explanation:

The n th term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₃ = 10 and a₅₁ = - 182, then

a₁ + 2d = 10 → (1)

a₁ + 50d = - 182 → (2)

Subtract (1) from (2) term by term to eliminate a₁

48d = - 192 ( divide both sides by 48 )

d = - 4

Substitute d = - 4 into (1) and evaluate for a₁

a₁ + 2(- 4) = 10

a₁ - 8 = 10 ( add 8 to both sides )

a₁ = 18