The 13th term of this geometric sequence is 16,384 and the first term is 4. what is the common ratio

1 answer:

3 0

A geometric sequence is a sequence with a common ratio multiplied by previous term to give the next. Lets call x the common ratio, so we know that 4 was multiplied by x to give the second term, and so forth until it was multiplied again and again by x until the 16384 was reached which happens to be the 13th term, that means that 4x was multiplied by x 12 more times to give 16384, that is:
4x^12 = 16384
x^12 = 4096
x = 4096^-12
x = 4.48 x 10^-44
that is the common ratio

You might be interested in

3x + 4y=17<br>- 4x – 3y = - 18

OleMash [197]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Label the equations in number 5-7 as True or False:

kkurt [141]

Answer:

${ \rm{ {(7}^{1}) ^{9 } = 7 {}^{5} \times {7}^{5} : \: { \tt{ \red{false}}} }} \\{ \boxed{ \mathfrak{correction \dashrightarrow \: ( {7}^{1}) {}^{9} = {7}^{9} }}} \\ \\ { \rm{ \frac{ {y}^{13} }{ {( {y}^{2}) }^{6} } = {y}^{ - 10} \times {y}^{9} : \:{ \tt { \red{false}}}}} \\ { \boxed{ \mathfrak{correction \: \dashrightarrow \: { \rm{{y}^{1} }}}}} \\ \\ { \rm{ {b}^{4} \times {b}^{ - 6} = \frac{ {b}^{1} \times {b}^{3} }{ {b}^{6} } }} \: : \: { \tt{ \green{true}}}$