Mathematics

Grade10

Easy

Question

# Find the 30^{th} term of the Arithmetic Sequences 10 , 7 , 4……..

- 77
- -77
- -87
- 87

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 sequence. We are asked to find the 30^{th} term. We will find the common difference first.

## The correct answer is: -77

### The given sequence is 10, 7, 4, …

The first term of the progression is a_{1 }= 10.

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 common difference is d = 7 – 10

d = -3

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

a_{n }= a + (n – 1)d

We will substitute n = 30 to find the 30^{th} term.

a_{30 }= 10 + (30 – 1)(-3)

= 10 + (29) (-3)

= 10 – 87

= -77

So, the 30^{th} term is -77.

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