Help with a Maths Problem

Hi, I'm doing homework and i dont know what to do???
The 17th term or an arithmetic sequence is 50 and the first term is 2... how do i find thw common difference???
Thanks in Advance :)

The nth term of an arithmetic series is given by a + (n - 1)d, where a is the first term and d is the common difference.

a = 2 and the 17th term is 50, so 2 + (17 - 1)d = 50.

This becomes 2 + 16d = 50, which simplifies to 16d = 48 => d = 3.

To get from the first term to the 2nd term, you add the common different 1 time.

2 - 1 = 1

To get to the 3rd term you would add the common difference to the 2nd term. At this point
you would have added the common differnce twice.

3 - 1 = 2


So to get from the 1st term to the 17th term how many times do you add the common difference

17 - 1 = 16


If we call the common difference n, then to get the 17th term we have

first term + 16 x n = 17th term. We know the first and 17th term

2 + 16 x n = 50 and so we can solve for the common difference.

Start by subtract 2 from both sides of the equation

16 x n = 48 and divide both sides by 16 to get n

n = 48/16 = 3

So the common difference is 3

use formula
an=a1+(n-1)d
set for a17
a17=a1+(17-1)d
but a1=20
then:
a17=20+(17-1)d
but a17=50
set
50=20+(16d)
.'. d=30/16

Hello

The formula is

un = u0 + (n-1)r

50 = 2 + 16r
16r = 48
r = 3

Hope it helps

Bye