Question

Two questions!! Please help!!

Would the 21st term of the geometric sequence that starts with 2, 6, 18, 54... be 6973568802?


Also, find the sum of the first six terms of the geometric sequence for which a2=0.7 and a3=0.49

Answer 1

Divde the previous term,

54/18 = 3

18/6 = 3

6/3 = 3


So the formula to find the 21 term is f(n) = f(1) • r^n-1

That's the explicit formula


The rate is 3
F(1) = 2


So simply plug in,

f(21) = 2 * 3^21-1

Can you solve from there?

Answer 2

Yes! I got the same answer I got before! Which is" 6973568802!

Answer 3

Ok then, it is right!

Answer 4

Thank you! Could you help me with the second one too, by chance? :3

Answer 5

sure

Answer 6

find the sum of the first six terms of the geometric sequence for which a2=0.7 and a3=0.49-- how would I go about doing this?

Answer 7

The formula for is, a_n=a_1•r^n−1.

Answer 8

The rate is 0.7, to find the rate your self divide 0.49/0.7


Now that you have your rate plug in,

a_6 = a_1 * 0.7^6-1

Answer 9

r=an/an-1
her r=a3/a2=0.49/0.7=0.7
a2=a1*r
0.7=a1*0.7
a1=0.7/0.7=1
s=(a1)(1-r^n)/(1-r)
n=7
find s

Answer 10

I got .117649 for my answer, but feel like that's not correct?