What is the sum of the first 100 terms of the sequence 4,9,14,19, ...?
2 answers:
Answer:
25150
Step-by-step explanation:
First, we have to see that this is an arithmetic sequence... since to get the next element we add 5 to it. (a geometric sequence would be a multiplication, not an addition)
So, we have a, the first term (a = 4), and we have the difference between each term (d = 5), and we want to find the SUM of the first 100 terms.
To do this without spending hours writing them down, we can use this formula:
If we plug in our values, we have:
S = 50 * (8 + 495) = 50 * 503 = 25150
You might be interested in
The total distance phoebe has to drive each day (round trip) while her usual route is closed is 42 miles
<h3>What is a Pythagoras theorem?</h3>The square of the longest side is equal to the square of the sum of the othersides.
Before we can calculate the total distance, we will need to get the hypotenuse on both sides using the Pythagoras theorem as shown:
H^2= 12^2 + 9^2
H² = 144 + 81
H² = 225
H = 15
For the other hypotenuse
h² = 12² + 5²
h² = 144 + 25
h² = 169
h = 13 mils
The total distance = 5 + 15 + 9 + 13
The total distance = 42 miles
The total distance phoebe has to drive each day (round trip) while her usual route is closed is 42 miles
Learn more on Pythagoras theorem here: brainly.com/question/12306722
a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is
b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so
c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so
Then by linearity, we have