Mathematics

Grade10

Easy

Question

# Which term of the Arithmetic Sequences: 27 , 24 , 21 ,........ is zero?

- 8th
- 10th
- 9th
- 11th

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 given a term from the sequence. We have to find the position of that term. We will find the common difference first.

## The correct answer is: 10th

### The given sequence is 27, 24, 21, …

The given term is 0. We have to find it’s position.

The first term of the progression is a_{1} = 27

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 = 24 - 27

d = -3

The formula for n^{th} term of a arithmetic progression is given as follows:

a_{n} = a_{1} + (n – 1)d

We will substitute the values.

a_{n} = 27 + (n – 1)(-3)

0 = 27 + (-3n + 3)

0 = 30 – 3n

Rearranging the terms.

30 – 3n = 0

3n = 30

n = 10

So, zero is the 10^{th} term of the given sequence.

For such questions, we should know the formula to find any number of the terms. We should also know about common difference.