What is the value of the following expression...
2-4+6-8+10-12+14-16+...-100
2 + 6 + 14 = 22
Add the negative numbers and take it from there.
how about writing it like this:
(2-4) + (6-8) + (10-12) + .... + (98 - 100)
the value of each bracket is -2 and you have 50 such brackets, so .....
To find the value of the given expression, we need to evaluate the sum of the numbers in the pattern.
The pattern alternates between subtraction and addition, with the numbers decreasing by 2 each time. We need to determine how many terms are in the sequence and then calculate the sum.
The first term is 2, and the common difference is -2 (subtracting 2 each time). The last term is -100, and we need to find the number of terms in the sequence.
To find the number of terms in an arithmetic sequence, we can use the formula:
n = (last term - first term) / common difference + 1
Applying this formula to our sequence:
n = (-100 - 2) / (-2) + 1
= -102 / -2 + 1
= 51 + 1
= 52
We find that there are 52 terms in the sequence.
The sum of an arithmetic sequence can be calculated using the formula:
S = (n/2) * (first term + last term)
Substituting the values:
S = (52/2) * (2 + (-100))
= 26 * (-98)
= -2548
Therefore, the value of the given expression is -2548.