Question

how to find the number of terms of A. P. 13,17,21....,213​

Answer 1

Solution

13, 17, 21, .........., 213 are in AP

$\text{Let } a_n = 213$

By using nth term of AP formula

$\tt a_n = a + (n - 1)d$

Here

→ First term a = 13

→ Common difference d = 17 - 13 = 4

Substituting the values in the formula

$\implies 213 = 13 + (n - 1)4$

$\implies 13 + (n - 1)4 = 213$

$\implies (n - 1)4 = 213 - 13$

$\implies (n - 1)4 = 200$

$\implies n - 1 = \dfrac{200}{4}$

$\implies n - 1 = 50$

$\implies n = 50 + 1$

$\implies \boxed{n = 51}$

Hence, there are 51 terms in AP.

Answer 2

Answer:

51

Step-by-step explanation:

Given: A.P 13,17,21....,213​

To find: Number of terms.

The relation between nth term ($a_{n}$) , first term$(a)$, common difference $(d)$ & number of terms $(n)$ is given by:

$a_{n} =a+(n-1)d$

Here,

$a=13,a_{n}=213, \\d=a_{2}-a_{1} \\=17-13\\=4$

Substituting all values we have:

$213=13+(n-1)4\\213=13+4n-4\\213=9+4n\\204=4n\\n=51$

Therefore, number of terms are 51.

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