Simultaneous equations (sequences)

[zezima]

Just had a OCR C2 maths exam.

Question : Geometric sequence has second term : 24, and sum to infinity of 150. Create a simultaneous equation and find the possible values of A (first term) and R (common ratio).

1 : 24 = a(r^1)

2 : 150= a/r-1

I had trouble trying to solve the equations, I first tried to create a as the subject in the first equation but came to a quadratic when I input the A=24/r into equation 2.

 

[pka]

Just had a OCR C2 maths exam.

Question : Geometric sequence has second term : 24, and sum to infinity of 150. Create a simultaneous equation and find the possible values of A (first term) and R (common ratio).
1 : 24 = a(r^1)
2 : 150= a/r-1.

It should be: \(\displaystyle ar=24~\&~\dfrac{a}{1-r}=150\)