A new sequence is formed by adding together the corresponding terms of a geometric sequence and an arithmetric sequence. the geometric sequence has a common ratio of 3 and the arthmetric sequence has a common difference of -2.

Question

The first two terms of the new sequence are 4 and 20.

how do you calculate the third term of the new sequence?

Answer 1

I will assume that you are adding the corresponding terms of each sequence, that is ..
new sequence:
t1 = a+a
t2 = a+d + ar
t3 = a+2d + ar^2
etc

so a+a = 4
a+d + ar = 20
but d=-2 and r=3

2a = 4
a = 2
So all is known

t3 = 2 - 4 + 2(9) = 16

check:
AS: 2, 0, -2, -4, ..
GS: 2, 6, 18, 54, ..

new sequence is :
4, 6, 16 , 50 ..
All looks good

Answer 2

What is the 21st term of the sequence with a1 = -5 and d = 6?