Question

What is the 43rd term of an arithmetic sequence with a rate of increase of -6 and a11 = 12?

Answer 1

for an arithmetic sequence you can write an explicit equation

a(n) = a(1) - 6n

so we can use the fact that a(11) = 12 to find what a(1) is in our sequence

12 = a(1) - 6(11)
12 = a(1) - 66
78 = a(1)

now we have the equation
a(n) = 78 - 6n

from here if you want the 43rd term just use n=43