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

QUESTION: 

a) Write first four terms of a sequence with first term 1 and Term-to-Term rule ‘add 11’.

b) Find the 15th term.

SOLUTION:

a)

First term = 1 (given)

As Term-to-Term Rule is ‘add 11’, so

Second term = First term + 11 ⇒ 1 + 11 = 12

Third term = Second term + 11 ⇒ 12 + 11 = 23

Fourth term = Third term + 11 ⇒ 23 + 11 = 34

Hence,

the sequence is

1,  12,  23,  34, …………

b) 

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 15th term, so 

n = 15

First term = 1

Term-to-Term Rule = +11

Put these values in equation (1)

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

15th term = 1 + (15 – 1) × 11

15th term = 1 + 14 × 11

15th term  = 1 + 154

15th term = 155

Thus, 15th term of a linear(arithmetic) sequence

1,  12,  23,  34, ……..

is 155