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3 years ago

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In a GEOMETRIC sequence, the first term is 21 and the common ratio is 2. Find the 15th term.

1 answer:

guajiro [1.7K]3 years ago

3 0

Answer:

344064

Step-by-step explanation:

hope it is well understood

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Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

1 year ago

10, 9, 10, 11, 13, 13,5<br> Mean<br> Median<br><br><br><br> what are the answers??

Galina-37 [17]

Mean: 8.29
Median: 10

4 0

3 years ago

Read 2 more answers

A cylindrical barrel has a radius of 7.6 ft. and a height of 10.8 ft. Tripling which dimensions will triple the volume of the ba

Flauer [41]

Tripling the height will triple the volume.

Formua is r^2 * $\pi$ * height.

If you triple the radius, you must still square it, so it will be 9 times bigger.

If you triple the height, then it will be 3 times bigger.

5 0

4 years ago

Nadya [2.5K]

Answer:

0.106

Step-by-step explanation:

100 meters= 382 feet (per hour)

60 minutes in an hour

60 seconds in a minute

382/60=6.34 inches per minute (rounded to nearest tenth)

1 minute = 6.34 inches

6.34 / 60 = 0.106 (rounded to nearest thousandth)

8 0

3 years ago

PLS HELPP ITS URGENT

WITCHER [35]

Answer:

Step-by-step explanation:

The angles between the parallel sides add up to 180 degrees.

So 180-70 = 110 degrees.

8 0

3 years ago

Read 2 more answers