find the nth term an of the geometric sequence a2=7 and a4 =1575?

Answer 1

1___2___3____4
a___ar__ar²___ar³

ar = 7
ar³ = 1575

r² = 225
r = 15

a = 7/15

n th term
ar^(n-1)
(7/15)(15)^(n - 1)
(7) (15)^(n - 2)

Answer 2

We want to find an 'r' value that works or a ratio value.
First, recall the formula:
a_n = ar^(n-1).

Now plug in 2 and 4:
a_2 = ar^(2-1)
7 = ar

a_4 = ar^(4-1)
1575 = ar^(3)
1575 = arr^(2)
1575 = 7r^2 (since ar = 7 from above)
225 = r^2
r = +/- 15.

Plugging into 7 = ar gives our a values of +/- 7/15

So we will have two possible answers:

1) a_n = 7/15 (15)^(n-1).
2) a_n = -7/15 (-15)^(n-1).

As required.

Please note the other solutions for this question are incorrect - they only present the positive solution please note that there are indeed two solutions and any answer not including both is incorrect.

Answer 3

nth term
(7/15)^(n-1)

Answer 4

a2=ar;a7=ar^6
(ar^6)/(ar)=1575/7
r^5=225
r=225^(1/5)
r=2.954
a(2.954)=7
a=7/2.954
=2.370
nth term=ar^(n-1)=2.370x2.954^(n-1)
=2.370x2.954^n/2.954^1
=0.8023x2.954^n