How to find an expression for nth term of Linear(Arithmetic) Sequence

Solved example to find an expression for nth term of given Linear(Arithmetic) Sequence

QUESTION:

Find an expression for the nth term of the following arithmetic/linear sequence

5, 8, 11, 14……..

SOLUTION:

METHOD 1:

Using nth term formula

nth term = First term + (n – 1) × Term-to-Term Rule —————-(A)

Here, the given sequence is

5, 8, 11, 14, …….

First term = 5 ————–(1)

And

8 – 5 = 3

11 – 8 = 3

14 – 11 = 3

So Term-to-Term Rule = +3 —————–(2)

Put values from equations (1) and (2) to equation (A)

nth term = First term + (n – 1) × Term-to-Term Rule —————-(A)

nth term = 5 + (n – 1) 3

nth term = 5 + 3n – 3

nth term = 3n + 2

So the expression for the nth term is 3n+2

METHOD 2:

Follow these steps.

1. Find the Term-to-Term Rule.

2. Work out what to add or subtract.

3. Put both bits together.

Given term

8-5=3, 11-8=3, 14-11=3 So Term-to-Term Rule is 3. Thus first term of formula will be 3n

n=1 ⇒ 3n=3.

What we add with 3 that gives us the first given term, that is, 5? Yes, its 2.

So the expression for the nth term is 3n+2

Its your turn now. Try out this practice question and share its answer in comment below. Let me see how you do.

Find an expression for the nth term of the sequence

2, 9, 16, 23,……..