Question

What is the 7th term of the geometric sequence where a1 = 1,024 and a4 = −16?

1

−0.25

−1

0.25

Answer 1

@ganeshie8

Answer 2

@am!rah

Answer 3

use\[an=a _{1}*r^{n-1}\]

Answer 4

This is the formula for a geometric sequence, where a1= first term, r=common rate

Answer 5

My problem is plugging them in :c

Answer 6

do you know what the common rate is?

Answer 7

opps it is actually called the "common ratio" my fault sorry

Answer 8

Yeah, i do. i just dont know how i plug them in xD i get confused on which numbers to put where.

Answer 9

ok so you are looking for the 7th term so n=7

Answer 10

a1= the first term (you were given)

Answer 11

Mhm. And i dunno r.

Answer 12

r = the common ratio

Answer 13

i think it might be -4.

Answer 14

ok so plug in :)

Answer 15

its giving me a really big number ;-; Im so confused.

Answer 16

the common ratio might not be -4 then

Answer 17

@satellite73

Answer 18

\(\large {
\begin{array}{rrllll}
term&value
\\\hline\\
a_1&1024\\
a_2&a_1\cdot r\\
a_3&a_2\cdot r\to (a_1\cdot r)\cdot r\\
a_4&a_3\cdot r\to (a_1\cdot r\cdot r)\cdot r\to -16
\end{array}\\ \quad \\\\ \quad \\
\implies a_1\cdot r^3=-16\implies r=? }\)

Answer 19

What.

Answer 20

\(\large {
\begin{array}{llll}
term&value
\\\hline\\
a_1&1024\\
a_2&a_1\cdot r\\
a_3&a_2\cdot r\to (a_1\cdot r)\cdot r\\
a_4&a_3\cdot r\to (a_1\cdot r\cdot r)\cdot r\to -16
\end{array}\\ \quad \\\\ \quad \\
\implies a_1\cdot r^3=-16\implies r=? }\)

Answer 21

"r" is the common multiplier, or "common ratio"

Answer 22

Yeahh, i said -4.

Answer 23

once you find the common ratio, and the 1st term, is given, then you can find pretty much any term in the sequence

Answer 24

:c i still dont get how to plug it in. can you show me?

Answer 25

well... is not -4.... recheck it

Answer 26

-2?

Answer 27

\(\bf a_1\cdot r^3=-16\implies 1024r^3=-16 \implies r=?\)

Answer 28

I GOT -0.25 For the answer. ;-;

Answer 29

well... how did you get -0.25 if you dunno the common ratio?

Answer 30

i thought it was -4 D;

Answer 31

well... let's try -4 r = -4
so that means \( \bf a_1\cdot (-4)^3=-16\implies 1024(-64)=-16\implies 65536\ne -16\)