Question

What is the 9th term of the geometric sequence where a1 = -5 and a6 = -5,120

Answer 1

do you know the formula for n'th term of geometric series ?

Answer 2

\(\Large a_n = a_1 r^{n-1}\)

plug in a1 = -5 and a6 = -5,120, n = 6

Answer 3

and find 'r'

Answer 4

where doe -5120 go in the formula

Answer 5

@hartnn

Answer 6

its the 6th term, so its \(\Large a_6 \)

when you plug in n=6
the left side = a_6 = -5120

Answer 7

\(\Large -5120 = -5 r^{6-1}\)
find r

Answer 8

-5120=-5r^5
where do i go after that

Answer 9

divide both sides by 5

Answer 10

i mean -5

Answer 11

1024=r^5

Answer 12

yup now take 5th root on both sides

Answer 13

how do you do that

Answer 14

you can use calculator , right ?

Answer 15

is it 4

Answer 16

yes!
r= 4

now use the same formula again to get 9th term
this time r= 9

Answer 17

\(\Large a_9 = a_1 r^{9-1} \\ \Large a_9 = -5 \times 4^8 = ...\)

Answer 18

ohhh

Answer 19

-327,680

Answer 20

\(\huge \checkmark \)

Answer 21

What is the sum of the arithmetic sequence 151, 137, 123, …, if there are 26 terms

Answer 22

could you find the common difference ?

Answer 23

its -14

Answer 24

thats correct,
d= -14
a1 = 1st term = 151
n = number of terms = 26

Answer 25

just use this formula directly
\(\Large S_n = (n/2) (2a_1 + (n-1)d)\)

Answer 26

-624?

Answer 27

\(\huge \checkmark \)

Answer 28

thank you so much

Answer 29

welcome ^_^