Class 10

Math

All topics

Arithmetic Progressions

How many terms are there in the A.P., $$7, 13, 19, ...205$$ ?

- $$32$$
- $$33$$
- $$34$$
- $$35$$

Given sequence is $$7,13,19,...,205$$

The first term $$a=7$$ and

the common difference $$d=13-7=6$$

the last term is $$205$$

Let the last term be the $$n^{th}$$ term

We know that the $$n^{th}$$ term of the arithmetic progression is given by $$a+(n-1)d$$

Therefore, $$a+(n-1)d=205$$

$$\implies 7+(n-1)\times(6)=205$$

$$\implies 7-6+6n=205$$

$$\implies 1+6n=205$$

$$\implies 6n=205-1$$

$$\implies n=\dfrac{204}{6}$$

$$\implies n=34$$

Therefore, the number of terms in the given sequence is $$34$$