What is the sum of the multiples of 4 from 16 to 100?
so you want
16+20+24+...100
number of terms = ??
you have an AS, where
a = 16 , d=4
term(n) = a+(n-1)d
100 = 16 + (n-1)(4)
84 = 4n - 4
88 = 4n
n = 22
so we want S(22)
= (22/2)(first + last) = 11(16+100) = 1276
Ooh, it's time to play "Let's Do Some Math with the Clown!" Alright, let's do this! To find the sum of the multiples of 4 from 16 to 100, we need to figure out how many multiples there are and then add them up. Now, let me put on my math hat, which is just a hat that says "I hate math." Alright, here we go!
The first multiple of 4 in this range is 16, and the last multiple is 100. So, to figure out how many multiples of 4 there are, we need to find out how many times we can add 4 to 16 to get to 100. And, for simplicity's sake, I'm not going to use a calculator because they always give me the wrong number.
So, let's see... 16 + 4 = 20... add another 4... 24... and so on until we reach 100. *thinking hard* Okay, there's 1... 2... 3... *counting on fingers* 4... 5... *holding up other hand* 6... 7... *realizing I'm running out of fingers* Uh-oh, hold on a second, let me take off my shoes and count on my toes... 8... 9... *struggling to remove shoe* Ahh, this is why I hate math!
But fear not! By putting on my ridiculously oversized clown shoes, I've actually managed to count all the way up to the 25th multiple of 4. So, there are 25 multiples of 4 in the range from 16 to 100. Now, all we have to do is add them up! And for that, I'll have to consult my trusty clown calculator... it's just a normal calculator with a red nose attached to it.
So, 4 + 8 + 12 + 16 + 20 + 24 + ... + 96 + 100... and after feverishly tapping the buttons on my clown calculator, I can tell you the sum of these multiples is 1300!
Yes, 1300! So, the sum of the multiples of 4 from 16 to 100 is 1300. Ta-da! Wasn't that a wild and mathematically thrilling ride?
To find the sum of the multiples of 4 from 16 to 100, we can use the formula for the sum of an arithmetic series:
Sum = (n/2)(first term + last term)
In this case, the first term is 16, the last term is 100, and the common difference is 4.
To find the number of terms (n), we can use the formula:
n = (last term - first term) / common difference + 1
n = (100 - 16) / 4 + 1
n = 84 / 4 + 1
n = 21 + 1
n = 22
Next, we can substitute the values into the formula for the sum:
Sum = (n/2)(first term + last term)
Sum = (22/2)(16 + 100)
Sum = 11(116)
Sum = 1276
Therefore, the sum of the multiples of 4 from 16 to 100 is 1276.
To find the sum of the multiples of 4 from 16 to 100, we can use a formula to calculate the sum of an arithmetic series.
First, we need to determine the first term (a), the common difference (d), and the number of terms (n) in the sequence.
In this case, the first term (a) is 16 since it is the smallest multiple of 4 in the given range.
The common difference (d) is also 4 since each subsequent term increases by 4.
To find the number of terms (n), we can use the formula: n = (last term - first term) / common difference.
So, in our case, the number of terms (n) is (100 - 16) / 4 = 84 / 4 = 21.
Using the formula for the sum of an arithmetic series:
Sum = (n/2) * (2a + (n-1)d)
Plugging in the values:
Sum = (21/2) * (2 * 16 + (21-1) * 4)
= (21/2) * (32 + 20 * 4)
= (21/2) * (32 + 80)
= (21/2) * 112
= 21 * 56
= 1176
Therefore, the sum of the multiples of 4 from 16 to 100 is 1176.