# maths question

The 2nd term of a geometric sequence is 3 +2√3
The 3rd term of the sequence is 19 + 13√3

Find the value of the common ratio of the sequence.

Give your answer in the form a - (√b)/c, where a, b and c are integers.

You must show all your working.

literally what is this 😭 im cooked
any help appreciated!
Original post by x-wing_pilot
The 2nd term of a geometric sequence is 3 +2√3
The 3rd term of the sequence is 19 + 13√3
Find the value of the common ratio of the sequence.
Give your answer in the form a - (√b)/c, where a, b and c are integers.
You must show all your working.
literally what is this 😭 im cooked
any help appreciated!

What is the common ratio of a GP?

Here's a GP 2, 6, 18, the common ratio is 18/6 = 3 each term is three times the one before.

so the common ratio of your GP is?
so it's 19 + 13√3 / 3 +2√3 ?
how do i do that without a calculator... sorry if its a dumb question lol im super bad at maths
Original post by x-wing_pilot
so it's 19 + 13√3 / 3 +2√3 ?
how do i do that without a calculator... sorry if its a dumb question lol im super bad at maths

https://www.symbolab.com/solver/simplify-calculator/simplify%20%5Cfrac%7B19%2B2%5Csqrt%7B3%7D%7D%7B3%2B2%5Csqrt%7B3%7D%7D?or=input
this is an online calculator, tells you the steps, but essentially, you multiply by 3 - 2√3 / 3 - 2√3 because it's like difference of two squares
this gets rid of the surd in the denominator and you expand the numerator
Original post by x-wing_pilot
so it's 19 + 13√3 / 3 +2√3 ?
how do i do that without a calculator... sorry if its a dumb question lol im super bad at maths

You rationalise the denominator ...