Question

Write down in terms of n, an expression for the nth term

of the following sequences
a) 25 20 15 10 5​

Answer 1

Solution,

First term (a) = 25

Common difference (d) = Second term - first term = 20 - 25 = -5

Now,

nth term = a + (n - 1)d = 25 + (n - 1) (-5) = 25 - 5n +5 = 30 - 5n

The nth term of the series is 30 - 5n

Answer 2

The nth term will be:

`a_n=-5n+30`

Explanation:

Given the sequence

25, 20, 15, 10, 5​

An Arithmetic sequence has a constant difference 'd' and is defined by

`a_n=a_1+\left(n-1\right)d`

Computing the common difference of all the adjacent terms

`25,\:20,\:15,\:10,\:5`

`20-25=-5,\:\quad \:15-20=-5,\:\quad \:10-15=-5,\:\quad \:5-10=-5`

As the difference between all the adjacent terms is the same and equal to

`d=-5`

Also, the first term is:

`a_1=25`

Hence, the nth term will be:

`a_n=a_1+\left(n-1\right)d`

`a_n=-5\left(n-1\right)+25` ∵
`a_1=25`,
`d=-5`

`a_n=-5n+30`

Therefore, the nth term will be:

`a_n=-5n+30`