Question

(viii) -25, -23, -21, -19, ...

Answer 1

(viii) In the given sequence, we have:
t₁ = –25, t₂ = –23, t₃ = –21 and t₄ = –19
Thus, we get:
t₁ = –25
t₂ = –23 = –25 + 2 = t₁ + 2 = t_{(2 – 1)} + 2
t₃ = –21 = –23 + 2 = t₂ + 2 = t_{(3 – 1)} + 2
t₄ = –19 = –21 + 2 = t₃ + 2 = t_{(4 – 1)} + 2
We have:
t_n = t_{(n – 1)} + 2
Now, to find the next four terms, we need to take n = 5, 6, 7 and 8.
Here,
t₅ = t_{(5 – 1)} + 2 = t₄ + 2 = –19 + 2 = –17
t₆ = t_{(6 – 1)} + 2 = t₅ + 2 = –17 + 2 = –15
t₇ = t_{(7 – 1)} + 2 = t₆ + 2 = –15 + 2 = –13
t₈ = t_{(8 – 1)} + 2 = t₇ + 2 = –13 + 2 = –11
Thus, the next four terms are –17, –15, –13 and –11.