Mathematics

Grade10

Easy

Question

# Determine the first term and common difference whose 3^{rd} term is 5 and the 7^{th} term is 9

- 3 , 1
- 4 , 2
- 5 , 3
- 1 , 3

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 third term and seventh term of a sequence. We are asked to find the first term and common difference.

## The correct answer is: 3 , 1

### The first term of the progression is denoted by "a"

The common difference is "d".

The third term is a_{3} = 5

The fifth term is a_{7} = 9

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 + (n – 1)d

Let’s see the formula for fifth and seventh term.

a_{3}= a + (3 – 1)d

5 = a + 2d …(1)

a_{7} = a + (7 – 1)d

9 = a + 6d …(2)

Solving the equations (1) and (2). We will subtract (1) from (2).

4d = 4

So, d = 1

We will substitute the value of d in equation (1).

5 = a + 2(1)

5 = a + 2

a = 3

So, the first term of the sequence is 3 and the common difference is 1.

The right option is 1,3.

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