Question

Given the following sequence, determine whether it is arithmetic progression or not. If it is an Arithmetic progression, find its general term.
–5, 2, 9, 16, 23, 30, ....

Answer 1

In the given sequence, we have:
t₁ = –5, t₂ = 2, t₃ = 9, t₄ = 16, t₅ = 23 and t₆ = 30
Thus, we get:
t₂ – t₁ = 2 – (–5) = 2 + 5 = 7
t₃ – t₂ = 9 – 2 = 7
t₄ – t₃ = 16 – 9 = 7
t₅ – t₄ = 23 – 16 = 7
t₆ – t₅ = 30 – 23 = 7

Because the difference between any two consecutive terms is constant, which is 7, the given sequence is an arithmetic progression.
We have:
First term, a = t₁ = –5
Common difference, d = 7

We know that the general term of an A.P. is t_n = a + (n – 1)d.
Thus, the general term of the given A.P. is:
t_n = –5 + (n – 1)7 = –5 + 7n – 7
$\Rightarrow$t_n = 7n – 12