What is the sum of the first 10 terms of the sequence defined by an=3n-3?

The sum of first 10 terms of the sequence defined by is 135.

Step-by-step explanation:

Given : nth term of a sequence as

We have to find the sum of first 10 terms of the sequence.

Consider the nth term of a sequence as

Then put n = 1  to get the first term

put n = 2 to get the next term

put n = 3 to get the next term

put n = 4 to get the next term

Thus, the sequence is of the form 0, 3, 6, 9,.....

Thus, the above is an arithmetic sequence with a = 0 and common difference (d) = 3

Thus, Sum of 10 terms is given by

n = 10 , a = 0 , d = 3

Put we get,

Simplify, we have,

Thus, the sum of first 10 terms of the sequence defined by is 135.

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.

arc length = 6.63311 ft.

step-by-step explanation:

the formula the arc measure is:

arc length s=2πr(c)/360

where:

c   is the central angle of the arc in degrees

r   is the radius of the arc

π   is pi, approximately 3.142

using the above formula we get

s =

thus we find that arc length of an arc for a circle of radius 20 feet and central angle 19 degrees is

6.63311 feet