General

General

Easy

Question

# Find the number of terms in the Arithmetic Sequences: 7 , 13 , 19 ,…….,205

- 34
- 24
- 35
- 40

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 till it’s last term. We are asked to find the number of terms in the sequence.

## The correct answer is: 34

### The given sequence is 7, 13, 19, … ,205

The first term of the progression is denoted by a_{1} = 7

The common difference is denoted by d.

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 = 13 – 7

= 6

The last term is 205.

Let the number of terms in sequence be n. We have to find the value of n.

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

a_{n }= a_{1 }+ (n – 1)d

205 = 7 + (n – 1)6

205 = 7 + 6n – 6

205 = 1 + 6n

Rearranging and subtracting 1 from both the sides we get,

6n = 204

n = 34

As n = 34, there are 34 terms in the given sequence.

For such questions, we should know the formula to find any number lf term.