Question

For an A.P,the first term is 5 and the last term ia 30.the sum of all the terms is 420 what is the value of n

Answer 1

If the first term and last term in A.P. is 5 and 30 respectively and the sum is 420, then the value of n is 24.  

Step-by-step explanation:

Let,  

“a” = the first term of an A.P. = 5

“l” = the last term of an A.P. = 30

“Sn” = the sum of n terms of an A.P. = 420

We know that the formula of the sum of n terms in A.P. is given by,

Sn = $\frac{n}{2}$ [a + l]

Now, substituting the given values in the above formula, we get

420 = $\frac{n}{2}$ * [5+30]

⇒ 420 = (n/2) * 35

⇒ n/2 = 12

⇒ n = 12 * 2

⇒ n = 24

Thus, the value of n is 24.

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Answer 2

The value of n is 24.

Step-by-step explanation:

Given : For an A.P, the first term is 5 and the last term is 30. The sum of all the terms is 420.

To find : What is the value of n ?

Solution :

The sum of n terms of an A.P is given by,

$S_n=\frac{n}{2}[a+l]$

Where, n is the number of terms

$S_n=420$ is the sum of n terms

a=5 is the first term

l=30 is the last term

Substitute the values,

$420=\frac{n}{2}[5+30]$

$840=35n$

$n=\frac{840}{35}$

$n=24$

Therefore, the number of terms is 24.

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