How to find missing terms of Linear(Arithmetic) sequence if first and any other term is given

How to find missing terms of Linear(Arithmetic) Sequence if FIRST and any other term is given

1, ____, ____, 7, ………

SOLUTION:

STEP 1: Find Term-to-Term Rule.

The formula for nth term of a Linear(Arithmetic) Sequence is:

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

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

Now,

First term = 1 (given)

For n=4, 4th term = 7 (given)

Put these values in equation (1)

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

4th term = 1 + (4 – 1 ) × Term-to-Term Rule

7 = 1 + 3 × Term-to-Term Rule

Subtract 1 on both sides

7 – 1 = 1 – 1 + 3 × Term-to-Term Rule

6 = 3 × Term-to-Term Rule

Divide by 3 on both sides

frac{6}{3} = frac{3}{3} × Term-to-Term Rule

2 = Term-to-Term Rule

Thus Term-to-Term Rule = 2

As it is positive, it means Term-to-Term Rule is ‘add 2’

STEP 2: Apply Term-to-Term Rule and find the missing terms.

Second term = First term + 2 ⇒ 1 + 2 = 3

Third term = Second term + 2 ⇒ 3 + 2 = 5

Hence the given linear(arithmetic) sequence is

1, 3, 5, 7, ……..