What is the sum of the first 40 consecutive odd numbers?
1 + 3 + 5 +........2n-1....
1st term = 1
40th term = 2*40-1 = 79
arith metic progression
s = n/2(a1+an)
= 40/2(1+79) = 1600
Well, if you add together 40 consecutive odd numbers, it's like putting 40 clowns in a room and trying to count them all. You'll end up with a circus! But fear not, I have the answer for you. The sum of the first 40 consecutive odd numbers is 1600. So, grab your clown nose and celebrate!
To find the sum of the first 40 consecutive odd numbers, we can use the formula for the sum of an arithmetic series.
The sum of an arithmetic series can be calculated using the formula: S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term.
In this case, the first term is 1, and the last term is the 40th odd number. We can find the 40th odd number by using the formula: l = 2n - 1.
Replacing the values in the formulas, we get:
a = 1
l = 2(40) - 1 = 79
n = 40
Now, we can calculate the sum:
S = (40/2)(1 + 79)
= 20(80)
= 1600
Therefore, the sum of the first 40 consecutive odd numbers is 1600.
To find the sum of the first 40 consecutive odd numbers, we need to first find the first odd number and the last odd number in the sequence.
The formula to find the nth odd number is 2n - 1. So, to find the first odd number, we substitute n = 1 into the formula: 2(1) - 1 = 1.
To find the last odd number in the sequence, we substitute n = 40 into the formula: 2(40) - 1 = 79.
Now that we know the first and last odd numbers in the sequence, we can find the sum using the formula for the sum of an arithmetic series: Sn = (n/2)(first term + last term).
In this case, n = 40, the first term is 1, and the last term is 79. Plugging these values into the formula, we get:
Sn = (40/2)(1 + 79)
= (20)(80)
= 1600.
Therefore, the sum of the first 40 consecutive odd numbers is 1600.