Question

the first term of an ap is 1 and nth term is 25 . if Sn=520 then n=?

Answer 1

Answer :

n = 40

Step-by-step explanation :

Given :

• first term of AP , a = 1
• nth term, aₙ = 25

To find :

• If Sₙ = 520, n = ?

Solution :

 Given first term and nth term.

nth term of AP is given by,

   aₙ = a + (n - 1)d

   25 = 1 + (n - 1)d

   25 - 1 = (n - 1)d

   (n - 1)d = 24

Sum of n terms is given by,

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

520 = n/2 [ 2(1) + 24 ]

520 × 2 = n [ 2 + 24 ]

1040 = n [26]

  n = 1040/26

  n = 40

∴ The value of n is 40