In a geometric sequence, a2= -144 and a5=486. write the explicit formula for this sequence

= 96

Step-by-step explanation:

The n th term of a geometric sequence is

= a

where a is the first term and r the common ratio.

Both values have to be found.

Using

a₂ = - 144, then

ar = - 144 → (1)

a₅ = 486, then

a = 486 → (2)

Divide (2) by (1)

=

r³ = - 3.375 ( take the cube root of both sides )

r = - 1.5

Substitute r = - 1.5 into (1)

- 1.5a = - 144 ( divide both sides by - 1.5 )

a = 96

Hence explicit formula is

= 96

.632

step-by-step explanation:

6 * 1/10 = 3/5

3*0.01 = 0.03

3/5 + 0.03 = .63

2*0.002 = .002

.63 + 0.002 = .632

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;