Mathematics

Grade10

Easy

Question

# Which term of the Arithmetic Sequences : 3 , 8 , 13 , 18 ………. , is 78 ?

- 15
- 14
- 17
- 16

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 the term. We will find the common difference first.

## The correct answer is: 16

### The given sequence is 3, 8, 13, 18, …

The term is 78. We have to find it’s position.

The first term of the progression is a = 3

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 = 8 – 3

d = 5

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

a_{n }= a + (n – 1)d

We will substitute the values.

a_{n }= 3 + (n – 1)(5)

78 = 3 + 5n – 5

78 = -2 + 5n

78 + 2 = 5n

5n = 80

n = 16

So, the given term is 16th term.

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