For some number, t, the first 3 terms of an

arithmetic sequence are

t + 2, 3t, 4t + 1

Which of the following is the numerical value of the 4th

term.

a₄ = 17

Step-by-step explanation:

The difference d between consecutive terms of an arithmetic sequence are constant, that is

a₂ - a₁ = a₃ - a₂, substituting values

3t - t - 2 = 4t + 1 - 3t

2t - 2 = t + 1 (subtract t from both sides)

t - 2 = 1 (add 2 to both sides)

t = 3

Thus

a₁ = t + 2 = 3 + 2 = 5

a₂ = 3t = 3 (3) = 9

a₃ = 4t + 1 = 4 (3) + 1 = 12 + 1 = 13

The first 3 terms of the sequence are

5, 9, 13 with

d = 9 - 5 = 13 - 9 = 4, thus

a₄ = 13 + 4 = 17