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How many terms are there in the A.P., $$7, 13, 19, ...205$$ ?
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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 $$34$$
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| Question Text | How many terms are there in the A.P., $$7, 13, 19, ...205$$ ? |
| Answer Type | Text solution:1 |
| Upvotes | 150 |
