Find the equation for the nth term where the first term is 8 and the common difference is -2

Answer 1

This is known as an Arithmetic Progression, or AP.

You take the first term, a1, and add (n-1)d the common difference, d, times one less than n

an = a1 + (n-1)d

Here d= -2, which is negative. That means the sequence or progression will decrease, by 2 with each succeeding term:

The sequence is a1, a2, a3, a4, a5, a6, a7, a8, ...an ....

= 8, 6, 4, 2, 0, -2, -4, -6, .... 8 + (n-1)(-2) ...

As n approaches infinity, an approaches negative infinity.

This is a sequence, not to be confused with a "series" The series is the sum of the terms of a sequence

S3 for the above sequence is 8+6+4=18

The formula for Sn = n(a1+an)/2 = the sum of the first & last terms multiplied by n/2

For n=3, S3 = 3(8+4)/2 = 18

Answer 2

a_n = a₁ + (n - 1)d

a₈ = 8 + (7)(-2)