Find the 77th term for each sequence(use the equation: an=a1+(n-1)d)

Mathematics

1 answer:

ivolga24 [154]3 years ago

3 0

Step-by-step explanation:

$an = a1 + (n - 1)d \\ d = a2 - a1 \\ a1 = 5 \\ a2 = 10 \\ d = 5 \\ an = 5 + (n - 1)5 \\ an = 5n \\ a77 = 5 \times 77 = 385$

For B

$a1 = 17 \\ a2 = 14 \\ d = 14 - 17 = - 3 \\ an = 17 + (n - 1) \times - 3 \\ an = 17 - 3n + 3 \\ an = 20 - 3n \\ a77 = 20 - 3 \times 77 \\ a77 = - 211$

You might be interested in

two angles of a triangle have equal measures for the third angles measure is 36 degrees less than the sum of the other two find

Effectus [21]

Answer: The first and second angles measure 54 degrees each. The third angle measures 72 degrees.

Step-by-step explanation:

First, I transcribed the sentences into equations.

The first part of the sentence says that "two angles of a triangle have equal measures", and we can use the konwledge that the interioir angle sum of all triangles in 180 degrees to solve this.

Lets call the first and second angles x and the third angle y. Then we can get the equation that 2x + y = 180. You might be asking "where did the 2x come from?", well, we know that if we add all of the angles up we get 180 degrees, and since two of the angles are equal, they can be simplified to 2x.

The second part of the sentence says that "the third angles measure is 36 degrees less than the sum of the other two", which translates to:

y = 2x - 36

Then we can substitute the second equation into the first and solve!

2x + (2x - 36) = 180

4x - 36 = 180

4x = 216

x = 54

Knowing that x = 54, we can substitute back into the first equation to solve for y. 2(54) + y = 180, 108 + y = 180, y = 72.

8 0

3 years ago

Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)

Ksivusya [100]

We first rewrite the line y - 3x = – 8 in <span>slope-intercept form as:

y=3x-8.

The form y=mx+n is called the "</span>slope-intercept form" because m tells us the slope and n tells us the y-intercept of the line.

Thus, the slope of the line is 3. We know that if a is the slope of any line perpendicular to our line, then the product of these slopes, 3a, is -1.

This means that the slope a is equal to -1/3. We are also given that the perpendicular line contains (3, 2). Thus, we write the equation:

$y-2= -\frac{1}{3}(x-3)\\\\y-2=-\frac{1}{3}x+1\\\\y=-\frac{1}{3}x+3$

Answer: $y=-\frac{1}{3}x+3$