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kirill [66]
2 years ago
11

What is the sum of the first 70 consecutive odd numbers? Explain.

Mathematics
1 answer:
expeople1 [14]2 years ago
5 0

The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)

The second sum is simply the sum of N ones:

\underbrace{1+1+1\ldots+1}_{N\text{ times}}=N

So, the final result is

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2

which ends the proof.

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If you get $0.75 everyday for 7 years and already have $4.35 (not counting leap years) how much money would you have at the end
Oksanka [162]

Step-by-step explanation:

7 years

leap years in 7 years:- 1

7 minus 1 equals to 6

6 calendar years to days:- 2190 days

so, $0.75 times 2190 = $1642.5

1642.5 plus $4.35 equals to 1646.85

7 0
3 years ago
Ying eats some yoghurt. The yoghurt contains 192 mg of calcium. This is 16% of the total amount of calcium that Ying should have
nikitadnepr [17]

Answer:

1200 mg

Step-by-step explanation:

16% = .16

.16x = 192

x =(192/.16)

x = 1200mg

4 0
2 years ago
Read 2 more answers
PLEASE HELP ASAP
zheka24 [161]

Answer:

the second forth and fifth on the graph.

Step-by-step explanation: have a good day!

5 0
2 years ago
Write an<br> explicit formula for An, the nth term of the sequence 7, -42, 252, ....
erik [133]

Answer:

A_n = 7(-6)^{n-1}

Step-by-step explanation:

<u>Key skills needed: Explicit formula, Geometric sequence</u>

1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.

This can be done by doing -42 ÷ 7   or   252 ÷ -42

-42 ÷ 7 equals -6.

252 ÷ -42 also equals -6.

2) This means that constant is -6.

3) The general form for an explicit formula of a geometric sequence is:

a_n = a_1(r)^{n-1}

--> r means the constant (or common ratio) that is being multiplied.

--> a_1 means the first term

--> a_n means the "nth" numbered term (so a_3 is the 3rd term, a_{10} is the 10th term and so on).

--> n-1 is just the "n" in a_n minus 1.

4) We can use this formula to create an explicit formula for the geometric sequence in the problem.

--> r = -6 (Since we got -6 as the constant/common ratio).

--> a_1  = 7 (Since 7 is the 1st term)

This means that our formula would be --> A_n = 7(-6)^{n-1}

<em>Hope you understood and have a nice day!! :D</em>

8 0
3 years ago
Is the figure an example of a segment?
Radda [10]

Answer: yes, it extends infinitely in opposite directions

Step-by-step explanation:

Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices, or otherwise a diagonal.

Let me know if this helped

5 0
2 years ago
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