Question

What is the nth term rule of the linear sequence below?

1
,
7
,
13
,
19
,
25

Answer 1

`a_(n)` = 6n - 5

Explanation:

There is a common difference d between the consecutive terms, that is

d =7 - 1 = 13 - 7 = 19 - 13 = 25 - 19 = 6

This indicates the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 1 and d = 6, thus

`a_(n)` = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5

Answer 2

Explanation:

t1 = 1 = 6 * 1 - 5

t2 =7 = 6 * 2 - 5

t3 = 13 = 6 * 3 - 5

t4 = 19 = 6*4 - 5

t5 = 25 = 6*5 - 5

-------------------------

Tn = 6n - 5

Hope it helped :)