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# Write the Sequence with Nth Term: an = 9 − 5n - CBSE Class 10 - Mathematics

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#### Question

Write the sequence with nth term: an = 9 − 5n

#### Solution

In the given problem, we are given the sequence with the nth term (a_n)

We need to show that these sequences form an A.P

an = 9 − 5n

Now, to show that it is an A.P, we will find its few terms by substituting  n = 1,2, 3

So

Substituting n = 1we get

a_1 = 9 - 5(1)

a_1 = 4

Substituting n = 2we get

a_2 = 9 - 5(2)

a_2 = -1

Substituting n = 3we get

a_3 = 9 - 5(3)

a_3 = -6

Further, for the given sequence to be an A.P,

Common difference (d)  = a_2 - a_1 = a_3 - a_2

Here

a_2 - a_1 = -1 - 4

= -5

Also

a_3  - a_2 = -6 - (-1)

= -5

Since a_2 - a_1 = a_3 - a_2`

Hence, the given sequence is an A.P.

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Solution Write the Sequence with Nth Term: an = 9 − 5n Concept: Arithmetic Progression.
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