The 4th term in an arithmetic sequence is 18 and 9th term is 43. Find the first 5 terms of the sequence

3, 8, 13, 18, 23

Step-by-step explanation:

The nth term of an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₄ = 18 and a₉ = 43 , then

a₁ + 3d = 18 → (1)

a₁ + 8d = 43 → (2)

Subtract (1) from (2) term by term, eliminating a₁

5d = 25 ( divide both sides by 5 )

d = 5

Substitute d = 5 into (1) for value of a₁

a₁ + 3(5) = 18

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

a₁ = 3 , then

a₂ = a₁ + 5 = 3 + 5 = 8

a₃ = a₂ + 5 = 8 + 5 = 13

a₄ = a₃ + 5 = 13 + 5 = 18

a₅ = a₄ + 5 = 18 + 5 = 23

The first 5 terms are 3, 8, 13, 18, 23