How to find nth term of decreasing Linear(Arithmetic) Sequence

QUESTION:

a) Write first four terms of a sequence with first term 40 and Term-to-Term rule ‘subtract 9’.

b) Find the 10th term.

SOLUTION:

First term = 40 (given)

As Term-to-Term Rule is ‘subtract 9’, so

Second term = First term – 9 ⇒ 40 – 9 = 31

Third term = Second term – 9 ⇒ 31 – 9 = 22

Fourth term = Third term – 9 ⇒ 22 – 9 = 13

Hence,

the sequence is

40, 31, 22, 13, …………

Let n = 1, 2, 3, …… gives us the position of terms of sequence.

Then the formula for finding nth term of a Linear(Arithmetic) Sequence is:

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

Here we have to find 10th term, so

n = 10

First term = 40

Term-to-Term Rule = – 9

Put these values in equation (1)

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

10th term = 40 + (10 – 1) × (- 9)

10th term = 40 + 9 × (- 9)

10th term = 40 – 81

10th term = – 41

Thus, 10th term of a linear(arithmetic) sequence

40, 31, 22, 13, …………

is – 41