Question

The first term of an A.P.is 1 and nth term is 25. If Sn = 520 ,then n = -

Answer 1

Answer:

Step-by-step explanation:

Given,

The first term (a) = 1, = 25 and = 520

To find, the value of n = ?

We know that,

The sum of up to nth term of an AP

=

∴ = 520

⇒ = 520

⇒ 13n = 520

Dividing both sides by 13, we get

=

⇒ n = 40

∴ n = 40

Answer 2

Answer

• n = 40

Given

• The first term of an A.P.is 1
• nth term is 25
• Sn = 520

To Find

• n = ?

Need's to know before solving

• nth term of an AP ,

$\bf a_n=a+(n-1)d\ \; \bigstar$

• Sum of n terms in AP ,

$\bf S_n=\dfrac{n}{2}[2a+(n-1)d]\ \; \bigstar$

Solution

Given ,

First term of AP ,

a = 1 ... (1)

nth term is 25 ,

$\implies \rm a_n=25\\\\\implies \rm a+(n-1)d=25\\\\\implies \rm 1+(n-1)d=25\ [From\ (1)]\\\\\implies \rm (n-1)d=24...(2)$

Sₙ = 520 ,

$\implies \rm \dfrac{n}{2}[2a+(n-1)d]=520\\\\\implies \rm \dfrac{n}{2}[2(1)+(n-1)d]=520\ [From\ (1)]\\\\\implies \rm \dfrac{n}{2}[2+(n-1)d]=520\\\\\implies \rm \dfrac{n}{2}[2+24]=520\ [From\ (2)]\\\\\implies \rm \dfrac{n}{2}[26]=520\\\\\implies \rm 13n=520\\\\\implies \bf n=40$