Question

for what value of n the ñth term of the AP 3,8,13.....,253​

Answer 1

Answer:

$\boxed{The\: value\: of \:n \:is \:51}$

Step-by-step explanation:

Given an AP -  3,8,13.....,253​

To find - The number of terms in the AP.

Here,

The first term , a = 3

           and

The comman difference, d = (a2- a) = (8 - 3) = 5

The last term or a(n) = 253

We know that ,

a(n) = a+ (n-1)d

When :- a(n) = 253, a = 3 and d = 5

253 = 3 + (n-1)5

253 = 3 + 5n - 5

253 = 5n - 2

∴ 5n = 253+2 = 255

n = 255/ 5 = 51

So, There are 51 terms in the AP 3,8,13.....,253​.

Answer 2

Step-by-step explanation:

• An = A + D (N-1)
• 253 = 3 + 5 (N-1)
• 253 = 3 + 5N -5
• 253= 5N -2
• 255 = 5N
• N = 51th Term

51th Term:

• A51 = 5(51) -2
• A51 = 255 - 2
• A51 = 253