Question

If an AP the first term is 3 and the last term is 20 the sum of all term is 460 what is the value of n?

Answer 1

GIVEN:

• First term of an A.P = 3
• Last term of an A.P = 20
• Sum of the terms = 460

TO FIND:

• Find the number of terms of an A.P ?

SOLUTION:

We have given that, an A.P has first term is 3 and the last term is 20 the sum of all term is 460.

To find the number of terms, we use the formula:-

$\large{\boxed{\bf{\star \: S_n = \dfrac{n}{2} [a + a_n] \: \star}}}$

According to question:-

On putting the given values in the formula, we get

➾ 460 = $\sf{ \dfrac{n}{2} \times}$ [3 + 20]

➾ 460 $\times$ 2 = n[ 23]

➾ 920 = 23n

➾ $\sf{\cancel\dfrac{920}{23}}$ = n

⠀⠀⠀⠀❛ n = 40 ❜

❝ Hence, the no. of terms of an A.P are 40 ❞

______________________

Answer 2

Given ,

• First term (a) = 3
• Last term (l) = 20
• Sum of first n terms = 460

We know that , the sum of first n terms of an AP is given by

$\boxed{ \sf{S_{n} = \frac{n}{2} (a + l)}}$

Thus ,

$\sf \mapsto 460 = \frac{n}{2} (3 + 20) \\ \\ \sf \mapsto \frac{460}{23} = \frac{n}{2} \\ \\\sf \mapsto 20 = \frac{n}{2} \\ \\\sf \mapsto n = 40$

$\therefore \underline{ \sf{The \: number \: of \: terms \: is \: 40 }}$