Question

62%

a) The nth term of a sequence is 2n - 3
Work out the first three terms of the sequence.
[2]
b) Write down an expression for the nth term of the following sequence.
9, 14, 19,
[2]
24,
BH

Answer 1

(a)
`Sequence: -1, 1, 3`

(b) nth term:
`T_n = 4+ 5n`

Explanation:

Solving (a)

Given

`T_n = 2n - 3`

The first 3 terms.

When n = 1

`T_1 = 2*1 - 3`

`T_1 = 2 - 3`

`T_1 = -1`

When n = 2

`T_2 = 2*2 - 3`

`T_2 = 4 - 3`

`T_2 = 1`

When n = 3

`T_3 = 3*2 - 3`

`T_3 = 6 - 3`

`T_3= 3`

So, the first three terms are:

`Sequence: -1, 1, 3`

Solving (b)

Given

`Sequence: 9,14,19,24`

Required

The nth term

The sequence is arithmetic.

So, first calculate the common difference (d)

`d = 14 - 9`

`d = 5`

The nth term is then calculated as:

`T_n = a + (n - 1) * d`

Where

`a =First\ term`

So:

`a = 9` and
`d = 5`

`T_n = 9 + (n - 1) * 5`

`T_n = 9 + 5n - 5`

Collect like terms

`T_n = 9 - 5+ 5n`

`T_n = 4+ 5n`