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tatiyna
3 years ago
8

2. Determine the sum of the first 400 ODD numbers.​

Mathematics
1 answer:
il63 [147K]3 years ago
3 0

Odd numbers take the form 2n-1, where n\ge1 is an integer. When n=400, the last odd number would be 799. So we're adding

S=1+3+5+\cdots+795+797+799

By reversing the order of terms, we have

S=799+797+795+\cdots+5+3+1

and we can pair up terms in both sums at the same position to write

2S=(1+799)+(3+797)+(5+795)+\cdots(795+5)+(797+3)+(799+1)

so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:

2S=400\cdot800\implies S=160,000

###

We could also make use of the formulas,

\displaystyle\sum_{i=1}^n1=n

\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2

We have

S=\displaystyle\sum_{i=1}^{400}(2i-1)=2\sum_{i=1}^{400}i-\sum_{i=1}^{400}1=400(400+1)-400=400^2=160,000

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x = 52

Step-by-step explanation:

28 + x - 4 + 2x = 180

Simplify the left side

3x + 24 = 180

Subtract 24 from each side

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Divide each side by 3

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3 0
2 years ago
A square with a side length of 5 inches has a area of 25 in<br><br> true or false
Goryan [66]

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TRUE

Step-by-step explanation:

5 x 5 = 25 in²

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3 years ago
You have $83 in your bank account each week you plan to deposit eight dollars from your allowance and $15 from your paycheck the
docker41 [41]
We know that you have 83$ in your bank account.

Okay so what is 15+8=23 So that means you get 23$ per week.

Now what is 83+23=106
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That means it would take 4 weeks for you to have 175 dollars in your bank account.
Hope this helped.
7 0
3 years ago
Solve: x^4-34x^2=-225
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8 0
3 years ago
If one root of the equation is 4x^2- 2x+p-4 be the reciprocal of other. then find the value of p​
SashulF [63]

Answer:

p = 8

Step-by-step explanation:

Let one root of the eqn. be alpha . Other root is 1/alpha .

We know that product of both roots of an quadratic eqn. is c/a where "c" is the co-efficient of the constant  & "a" is the co-efficient of x^2.

Here "c" is p-4 & "a" is 4. And the product of roots is 1 ( ∵ prdouct of a number and its reciprocal is 1 )

\frac{c}{a} = 1\\=> \frac{p - 4}{4} = 1\\=> p - 4 = 4\\=> p = 4 + 4 = 8

5 0
3 years ago
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