Question

the third term of an arithmetic sequence is 21, the eighth term is 56. the first term is….

Answer 1

if a is the first term we have

3rd term = a + 2d = 21
8th term = a + 7d = 56


solve this system of equations to find a and d

Answer 2

remember that
nth term = a + (n-1)d

where d = common difference, a = first term

Answer 3

where does the 2 and 7 come from?

Answer 4

n-1 in a + (n-1)*d

for 3rd term, n = 3 so n-1 = 2

Answer 5

okay so was the first term 7?