Write an explicit and recursive rule for the geometric sequence -5, 10, -20, 40… and use it to find the 12th

See solutions below

Step-by-step explanation:

Given the sequence -5, 10, -20, 40...

The nth term of the GP is expressed as;

Tn = ar^n-1

a is the first term

r is the common ratio

n is the number of terms

From the sequence, a = -5

r = 10/-5 = -20/10 = -2

Substitute

Tn = -5(-2)^n-1

This gives the explicit formula

For recursive;

a1 = -5

a2 = 10 = -2(-5) = -2a1

a3 = -20 = -2(10) = -2a2

From the shown sequence, we can see that;

an = -2an-1

This gives the recursive formula

Get the 12th term;

Using the explicit formula

T12 = -5(-2)^12-1

T12 = -5(-2)^11

T12 = -5(-2048)

T12 = 10240

Hence the 12th term is 10240