# Math Help - I want check my answers

1. ## I want check my answers

Hi all

Q 1 - Finif the sum of all integers between 1 and 100 inclusive ?
firist tearm a1 = 1 d = 2
an = a1 + (n - 1 ) d
1 + ( n-1 )s = 100
n-1 = 99/2 = 48.5
then : S48.5 = 48.5/2 (2(1) + ( 48.5-1)2)
= 0.25
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Q2 : An object falling from rest in a vacuum near the surface of the Eath falls 16 feet during the first second , 48 feet during the second , 80 feet during the third second
How far will the object fall in t second ?
S16 = a1 + ( n-1 ) d
16 + ( 15 ) (32)
= 496

2. Originally Posted by r-soy
Hi all

Q 1 - Finif the sum of all integers between 1 and 100 inclusive ?
firist tearm a1 = 1 d = 2
an = a1 + (n - 1 ) d
1 + ( n-1 )s = 100
n-1 = 99/2 = 48.5
then : S48.5 = 48.5/2 (2(1) + ( 48.5-1)2)
= 0.25
Do you really need someone to check this for you? 1+ 2+ 3+ ... [b]cannot[b] be less than 1!

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Q2 : An object falling from rest in a vacuum near the surface of the Eath falls 16 feet during the first second , 48 feet during the second , 80 feet during the third second
How far will the object fall in t second ?
S16 = a1 + ( n-1 ) d
16 + ( 15 ) (32)
= 496
Okay, this is an arithmetic series so you can use that formula. But why are you taking n= 16? You were asked to find how far the object will fall in t seconds. Don't you think that will depend on t?

3. Originally Posted by r-soy
Hi all

Q 1 - Finif the sum of all integers between 1 and 100 inclusive ?
firist tearm a1 = 1 d = 2
an = a1 + (n - 1 ) d
1 + ( n-1 )s = 100
n-1 = 99/2 = 48.5
then : S48.5 = 48.5/2 (2(1) + ( 48.5-1)2)
= 0.25
-------------------------------
Q2 : An object falling from rest in a vacuum near the surface of the Eath falls 16 feet during the first second , 48 feet during the second , 80 feet during the third second
How far will the object fall in t second ?
S16 = a1 + ( n-1 ) d
16 + ( 15 ) (32)
= 496
1. You should check your answers, do you think the sum of 1 to 100 is 0.25? Not sure where you get a common difference of two from, the integers are the whole numbers.

Spoiler:
a = 1
d = 1
n = 100

$S_n = \frac{n}{2}(2a+(n-1)d)$

I get an answer of 5050.

You could also have used the properties of triangular numbers, that is $S_n = \frac{n(n+1)}{2}$

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2. You want an answer in terms of t, not a numerical answer

Define downward direction as positive.
This would appear to be an arithmetic sequence with common difference 32

In this case t is much the same as n

Spoiler:
$U_t = a + (t-1)d = 16+31t$

4. thanks a lot