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3 years ago

Pattern in this sequence 1,1+3,1+3+5,1+3+5+7, ...

Mathematics

1 answer:

scoray [572]3 years ago

4 0

Answer:25

Step-by-step explanation:

1 , 1+3 ,1+3+5 ,1+3+5+7,_

1 , 4 , 9 , 16 ,_

From 1 to 4 there is a difference of 3

From 4 to 9 there is a difference of 5

From 9 to 16 there is a difference of 7

From 16 to x there should be a difference of 9 because all the differences mentioned above are all odd numbers so that is the pattern in the sequence

16+9=25

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Read 2 more answers

Find the exact value of cos theta, given that sin thetaequalsStartFraction 15 Over 17 EndFraction and theta is in quadrant II.

vova2212 [387]

Answer:

$cos \theta = -\frac{8}{17}$

Step-by-step explanation:

For this case we know that:

$sin \theta = \frac{15}{17}$

And we want to find the value for $cos \theta$ , so then we can use the following basic identity:

$cos^2 \theta + sin^2 \theta =1$

And if we solve for $cos \theta$ we got:

$cos^2 \theta = 1- sin^2 \theta$

$cos \theta =\pm \sqrt{1-sin^2 \theta}$

And if we replace the value given we got:

$cos \theta =\pm \sqrt{1- (\frac{15}{17})^2}=\sqrt{\frac{64}{289}}=\frac{\sqrt{64}}{\sqrt{289}}=\frac{8}{17}$

For our case we know that the angle is on the II quadrant, and on this quadrant we know that the sine is positive but the cosine is negative so then the correct answer for this case would be:

$cos \theta = -\frac{8}{17}$

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3 years ago