The second term of a GP is12 more than the first term,given that the common ratio is half of the first term.Find the third term of the GP?

Answer 1

"The second term of a GP is12 more than the first term"
-----> ar - a = 12
"the common ratio is half of the first term" ------> r = a/2 or a = 2r
put that back into ar-a = 12
2r(r) - 2r = 12
r^2 - r - 6 = 0
(r-3)(r+2) = 0
r = 3 or r = -2

if r = 3, the a = 6, third term = ar^2 = 6(9) = 54
if r = -2 ........ (your turn)

Answer 2

Why did you not finish the mathematics

Answer 3

Thanks a bunch

Answer 4

I can't solve it

Answer 5

The secon term of a GP is 12 more than the first term given that the common ratio is half of the first term find the third term of the GP.

Answer 6

I really love this app and everything that it entails the -2 can't be used as the common ratio because it is negative so the positive one will work perfectly

Answer 7

For r=-2 the answer is-0•75

Answer 8

You are a bonkon,why didn't you finish the solving

Answer 9

good results

Answer 10

T2=12+a
R=1/2 *a
Un=arn-1
12+a=a*1/2a
12+a=a²/2
Multiply both sides by two
24+2a=a²
Rearrange it
a²-2a-24=0
Then factorise.the factors are -6 and 4
a² -6a+4a-24=0
(a²-6a)(4a-24)=0
a(a-6)+4(a-6)
(a+4)(a-6)
a=-4 or a=6
Using the positive answer 6
T2=12+a=12+6=18
r=1/2*a=1/2*6=3
So therefore
T3=arn1
T3=6*3³–¹
T3=6*3²
T3=6*9
T3=54

Answer 11

I also need an answer to this.

Answer 12

Is this one mad. Finish the solution.💀