Question

What is the nth term for the sequence 1, 8, 15, 22, 29

Answer 1

7n-6

Explanation:

Work out the difference of the sequence:

8-1=7

Now you have the first part of the equation: 7n

n is the number that the integer is on the sequence

In this case:

1 = 1 as 1 is the first number of the sequence

And 2 = 8 as 8 is the 2nd number of the sequence

To find the full equation:

Do 7x1 to get you 7

Now see how far the 1st number is from 7

In this case you would do:

7-1 which gives you 6

Since you subtracted it to find the difference, it would be:

- 6

Therefore your answer would be 7n-6

To check it:

Times 7 by let's say 3 to get you 21

Then subtract 6 to get 15.

This is proven right as the 3rd number of the given sequence is 15.

Hope this helped

Answer 2

`a_(n)` = 7n - 6

Explanation:

there is a common difference between consecutive terms , that is

8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = 7

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 and d = 7 , then

`a_(n)` = 1 + 7(n - 1) = 1 + 7n - 7 = 7n - 6