Find the sum of the first 50 terms of the sequence 2,4,6,8........
That is twice the sum of 1+2+3+...+50
For 1+2+...+N, the sum is N(N+1)/2
The sum is therefore 2*[50*51)/2) = 2550
Ah, yes! Finding the sum of that sequence is like finding a clown in a room full of balloons - quite easy! Now, let's do some clown math.
We have a sequence that starts at 2, and each subsequent term increases by 2. It's like a never-ending parade of even numbers!
To find the sum of the first 50 terms, we can use the formula for the sum of an arithmetic sequence: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference.
In our case, n = 50, a = 2, and d = 2. Plugging these values into the formula, we get:
S50 = (50/2)(2 + (50-1)2)
= 25(2 + 49*2)
= 25(2 + 98)
= 25(100)
= 2500
Haha! So the sum of the first 50 terms of our sequence is 2500. That's quite a clownish sum, don't you think?
To find the sum of the first 50 terms of the sequence 2, 4, 6, 8, ..., you can use the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is given by: S = (n/2)(2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.
In this case, the first term (a) is 2, the common difference (d) is 2, and we have 50 terms (n) in total. So, plugging in these values into the formula, we have:
S = (50/2)(2 + (50-1)(2))
= 25(2 + 49(2))
= 25(2 + 98)
= 25(100)
= 2500
Therefore, the sum of the first 50 terms of the sequence 2, 4, 6, 8, ... is 2500.
To find the sum of the first 50 terms of the sequence 2, 4, 6, 8, ......, we can use a formula to find the sum of consecutive numbers.
The formula for finding the sum of consecutive numbers is given by: sum = (first term + last term) * number of terms / 2
In this sequence, we can see that the first term is 2 and the last term is 100 (since the sequence increases by 2 each time and we want the 50th term). So we have: sum = (2 + 100) * 50 / 2
Simplifying this equation, we get: sum = (102) * 50 / 2
Now, we can calculate the sum: sum = 102 * 25
The sum of the first 50 terms of the sequence is 2550.