Question

the first term of an arithmetic sequence is a b and the second term is a c. What is the explicit formula to find the nth term of the sequence?

Answer 1

Step-by-step explanation:

every new term is created by adding a constant (I call here x) to the previous term.

a1 = b

a2 = c = a1 + x = b + x

a3 = a2 + x = a1 + 2x = b + 2x

so, we see

an = a1 + (n-1)x = b + (n-1)x

from a1 and a2 we know

c = b + x

x = c - b

so, ultimately we have

an = b + (n-1)(c-b)