Question

Here are the 1st five terms of a number sequence.

3 7 11 15 16

a) work out the 8th term of the number sequence.
b) write down an expression, in terms of n, for the nth term of the number sequence.

Answer 1

see explanation

Explanation:

Note there is a common difference d between consecutive terms, that is

d = 7 - 3 = 11 - 7 = 15 - 11 = 19 - 15 = 4, thus sequence is

3, 7, 11, 15, 19, 23, 27, 31 ← with 8 th term = 31

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 a ₁ = 3 and d = 4, thus

`a_(n)` = 3 + 4(n - 1) = 3 + 4n - 4 = 4n - 1

Answer 2

A. 31

B. 4n - 1

Explanation:

A + (n-1)d

(a is the first term of the sequence, and d is the common difference)

= 3 +(8 - 1)4

= 3 + 7(4)

= 3 + 28 = 31

= a + (n-1)d

= 3 + (n-1)4

= 3 + 4n - 4

=4n - 4 + 3

= 4n - 1