Question

What arithmetic sequence with a_{4}=18 and a_{10}=48

Answer 1

Answer:

$a_{n}$ = 5n - 2

Step-by-step explanation:

the nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₄ = 18 and a₁₀ = 48 , then

a₁ + 3d = 18 → (1)

a₁ + 9d = 48 → (2)

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

6d = 30 ( divide both sides by 6 )

d = 5

substitute d = 5 into (1) and solve for a₁

a₁ + 3(5) = 18

a₁ + 15 = 18 ( subtract 15 from both sides )

a₁ = 3

Then

$a_{n}$ = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2