Question

Find the first five terms of the geometric sequence whose constant ratio is -5 and whose first term is 6.

Answer 1

Answer: 6,-30,150,-750,3750

Explanation:

Geometric progression formula is

An=a1r^(n-1)

An= nth term

A1= first term

R= common ratio

N= nth position

A1=6

R=-5

We already know the first term,looking for 2nd 3rd 4th & 5th

A2=a1r^(n-1)

A2=6×(-5^(2-1))

A2=6×(-5^1)

A2=6×-5

A2= -30

A3=a1r^(n-1)

A3=6×(-5^(3-1))

A3=6×(-5^(2))

A3=6×(25)

A3= 150

A4=a1r^(n-1)

A4=6×(-5^(4-1))

A4=6×(-5^3)

A4=6×-125

A4= -750

A5=a1r^(n-1)

A5=6×(-5^(5-1))

A5=6×(-5^(4))

A5=6×(625)

A5=3750

The first 5 numbers are

6,-30,150,-750,3750

Answer 2

Answer: 6, -30, 150, -750 and 3750.

Explanation:

First term= 6

Second term= ar = 6×(-5)= -30

Third term= ar^2 = 6×(-5)(-5) = 150

Forth term= ar^3 = 6×(-5)^3 = -750

Fifth term= ar^4 = 6×(-5)^4 = 3750