Question

What is the value of the 11th term in the following geometric sequence?

-5, -10, -20, -40



-5,120

-100

-180

-19,531,250

Answer 1

can u find the common ratio ?

Answer 2

if the common ratio is (r)
and
a_1 = -5
a_ 2 = -10
\[r = \frac{ a_{2} }{ a_{1}}\]

Answer 3

Isnt the common ratio 2?

Answer 4

after u find r .. u can use the general formula for a geometric progression
\[T_{n} = a \ r^{n-1}\]
where
a = the first term = a_1= (-5)
n = the nth term = in ur case 11
r = common ration = 2 ( yep u r correct! its 2)
can u find it now ?

Answer 5

\[T_{11}= (-5) \times 2^{11 - 1}\]

Answer 6

So you take An= -5 x 2 (n-1)

Answer 7

yep!

Answer 8

So what N?

Answer 9

n = the n th term or the position of the term u want to find

Answer 10

So how do we find N?

Answer 11

u know the n... it;s the problem.. they ask the value of the term which is positioned at the 11th place in this sequence..
so... n = 11
got it :) ?

Answer 12

So AN = -5 x 2 (11-1=10) Then you take 10and add it too 2?

Answer 13

u have to find the 10th power of 2
\[2^{10}\]
and multiply it by (-5)

Answer 14

so 20 x -5?

Answer 15

2x 10 = 2 multiply by 10 and its not what i mean
10 th power of 2 = 2 to the power 10 = 2x2x2x2x2x2x2x2x2x2 = ?

Answer 16

1,024

Answer 17

yep ... now multiply it by (-5)

Answer 18

got it :) ?

Answer 19

So 1,024 by -5?

Answer 20

So the answer is 5120?