Question

-2, 7, 16 ..... Determine the general rule (Tn) for this sequence ​

Answer 1

`T_(n)` = 9n - 11

Explanation:

There is a common difference between consecutive terms, that is

7 - (- 2) = 16 - 7 = 9

This indicates the sequence is arithmetic with nth term

`T_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 2 and d = 9 , then

`T_(n)` = - 2 + 9(n - 1) = - 2 + 9n - 9 = 9n - 11

Answer 2

It is Tn = 9n - 11

Explanation:

It is an arithmetic progression:

`T_(n) = a + (n - 1)d`

a is the first term, a = -2

n is number of terms

d is common difference, d = 7-(-2) = 9

`T_(n) = - 2 + \{ (n - 1) * 9 \} \\ T_(n) = - 2 + 9n - 9 \\ T_(n) = - 11 + 9n \\ T_(n) = 9n - 11`