# maths

posted by .

If told that the 3rd term of a GP is 36 and the 8th term is 8748. find the first term and the common ration.

• maths -

4 12 36 for the 3rd

• maths -

The n - th term of a geometric progression with initial value a and common ratio r is given by:

an = a * r ^ ( n - 1 )

In this case :

a3 = a * r ^ ( 3 - 1 ) = a * r ^ 2 = 36

a8 = a * r ^ ( 8 - 1 ) = a * r ^ 7 = 8748

So you must solve two equations :

a * r ^ 2 = 36

and

a * r ^ 7 = 8748

a * r ^ 2 = 36 Divide both sides by r ^ 2

a * r ^ 2 / r ^ 2 = 36 / r ^ 2

a = 36 / r ^ 2

a * r ^ 7 = 8748 Divide both sides by r ^ 7

a * r ^ 7 / r ^ 7 = 8748 / r ^ 7

a = 8748 / r ^ 7

a = a

36 / r ^ 2 = 8748 / r ^ 7 Multiply both sides by r ^ 7

36 * r ^ 7 / r ^ 2 = 8748 * r ^ 7 / r ^ 7

36 * r ^ 5 = 8748 Divide both sides by 36

36 * r ^ 5 / 36 = 8748 / 36

r ^ 5 = 243

r = fifth root ( 243 )

r = 3

a = 36 / r ^ 2

a = 36 / 3 ^ 2 = 36 / 9 = 4

OR

a = 8748 / r ^ 7

a = 8748 / 3 ^ 7 = 8748 / 2187 = 4

The first term of a GP:

a = 4

The common ratio:

r = 3

## Similar Questions

1. ### Maths

The 3rd term of an AP is 10 more than the first term while the fifth term is 15 more than the second term.find the sum of the 8th and 15 term of AP.if the 7th term is seven times the first term.
2. ### math

The 8th term of ap is 5time the 3rd term, while the 7th term is greater than the 4th term, write the first 5 term of the ap
3. ### maths

The sum of the 3rd and 7th term of an A.P is 38 and the 9th term is 37..Find the first term and common difference
4. ### Maths

The second term of a GP is 12, more than the first term, given that the common ratio is half of the first. Find the 3rd term of the GP
5. ### Mathematics

The 8th term of a linear sequence is 18th and 12th term is 26.find the first term and the common difference and 2th term
6. ### Maths

The sixth term of GP is 16 and the third term is 2.Find the first term and common ratio. 6th term =16 3rd term=2 So ar^5=16 and ar^2=2, then divide. So r^3=8, and r^3 =2^3. Therefore r =2 and a=1/2
7. ### maths

The 12th term of exceeds the 3rd term by 36 of an a.p If it's 16th term is 64 find first term and common difference
8. ### Further maths

The 8th term of a linear sequence is 18th and the 12th term is 26th .find the first term,common difference and the 20th term
9. ### maths

The 8th term of an ap is 5times the 3rd while the 7th term is 9 greater than the 4th term.write the first 5 terms.
10. ### FURTHER MATHS

The 8th term of a linear sequence is 18 and 12th term is 26.find the first term,common difference and 20th term

More Similar Questions