Question

The sum of an infinite GP is 6. The Sum of the first two terms is 4.5. What is the first term

Answer 1

I've done this but my answer is wrong

Answer 2

because my r was root -2

Answer 3

Hmmm, my guess is: \[
a+ar = 4.5\\
6=\frac{a}{1-r}
\]

Answer 4

thats what i got

Answer 5

what is your answer

Answer 6

First I do:\[
r = 1-\frac{a}{6}
\]

Answer 7

then\[
a\left(1+\left(1-\frac a6\right)\right) = 4.5
\]

Answer 8

it's a quadratic equation I guess.

Answer 9

so 9 or 3

Answer 10

sum to infinity is a/1-r => first term and second terms are a,ar

a(1+r) = 4.5 - eq1

a/1-r = 6 - eq2

eq1/eq2

1-r2 = 4.5/6 = 3/4

r2 = 1/4

r = 1/2 or -1/2

a(3/2) = 6

a =4 or 12

Hope its Correct...

Answer 11

Ahahaha.

Answer 12

Isn't That Correct? :\

Answer 13

not a choice for the answers