Mathematics

Grade10

Easy

Question

# What is the difference between the 20^{th} term and 40^{th} term of the Arithmetic Sequences with first term 5 and common difference 2?

- 20
- 40
- 50
- 110

Hint:

### The given question is about arithmetic progression. Arithmetic progression is a sequence of numbers where, the difference between two consecutive terms is constant. We are given the first term and the common difference. We are asked to find the difference between 20^{th} and 40^{th} term of the sequence.

## The correct answer is: 40

### The first term of the progression is a_{1 }= 5

The common difference is d = 2

Common difference is the fixed difference between the consecutive numbers of the sequence. We have to add the common difference to the preceding term, to get the next term. It can be negative or positive number. It can also have value zero.

The formula for nth term of a arithmetic progression is given as follows:

a_{n} = a_{1} + (n - 1) d

For 20^{th} term n = 20.

Substituting the values in above equation we get,

a_{20} = 5 + (20 - 1) 2

= 5 + 38

= 43

Similarly ,

a_{40} = 5 + (40 - 1)2

= 5 + 78

= 83

The difference between the 40^{th} term and 20^{th} term is

Difference = a_{40} - a_{20}

= 83 – 43

= 40

So, the difference between the 40^{th} term and 20^{th} term is 40.

For such questions, we should know the formula to find any number of the terms.