Question

the seventh term of a arithmetic sequence is 72 and the tenth term of the sequence is 90. if the sequence is defined by a formula f(n), then find f(2). How would you do this?

Answer 1

fn = a + d(n-1)

f(7) = a + 6 d = 72

f(10) = a + 9 d = 90

so
3 d = 90 - 72 = 18

d = 6

a + 6*6 = 72

a = 36
so our sequence is
f(n) = 36 + 6(n-1)
f(2) = 36 + 6(1)
f(2) = 42