Question

Write down in terms of n an expression of the nth terms?

Answer 1

The expression of the nth term can be written using the formulas

A. nth term =
`4 + (n-1)(-3)`

B. nth term =
`-7 + (n-1)(-5)`.

The expression of the nth term can be written as:

For the sequence 4, 1, -2, -5, -8............................

the first term a = 4 and the common difference d = -3.

aₙ =
`a + (n-1) d`

aₙ =
`4 + (n-1)(-3)`

Therefore, the nth term is given by the formula aₙ =
`4 + (n-1)(-3)`.

For the sequence -7, -12, -17, -22, -27...................

the first term a = 7 and the common difference d = -5.

aₙ =
`a + (n-1) d`

aₙ =
`-7 + (n-1)(-5)`

Therefore, the nth term is given by the formula aₙ =
`-7 + (n-1)(-5)`.

Answer 2

A. nth term = 4 + (n - 1) -3

B. nth term = -7 + (n - 1) -5

Explanation:

A. 4, 1, -2, -5, -8

First term, a = 4

Common difference, d = 1 - 4 = -3

nth term = a + (n-1)d

nth term = 4 + (n - 1) -3

B. -7, -12, -17, -22, - 27

First term, a = -7

Common difference, d = -12 - (-7)

= -12 + 7

= -5

nth terms = a + (n - 1)d

nth term = -7 + (n - 1) -5