Question

If there is an arithmatic sequence where a7= 12 and a19=-36 how do you find the general nh term formula for the 32nd term?

Answer 1

a7 = a1 + 6*d
a19 = a1 + 18*d
a32 = a1 + 31d

i) 12 = a1 + 6d
ii) -36 = a1 + 18d
iii) a32 = a1 + 31d

i - ii:
12 - (-36) = a1 + 6d - (a1 + 18d)
48 = - 12d
iv) d = -4

iv -> i:
12 = a1 + 6*(-4)
12 = a1 - 24
a1 = 36

iii) a32 = (36) + 31*(-4)
a32 = -88

Answer 2

thank you vitor023