Answer:
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
