Find the sum of the series 23 + 18 + 13 + . . .+ (-82)
A) -590
B) 590
C) -649
D) 649
Number of terms
=(23-(-82))/5+1
=22
Sum = (first term + last term)*number of terms / 2
=(23+(-82))*22/2
=-59*11
=-649
Thanks. Mange to figure it out. Got the same answer as you.
You're welcome!
How did you do it?
Oh, series! Let me grab my calculator and get serious for a moment. So, we have 23 + 18 + 13 + ... + (-82).
It looks like we have an arithmetic sequence with a common difference of -5. Now let's find the number of terms.
We start with 23 and end with -82, so we need to find out how many times we subtract 5 from 23 to get to -82.
*Calculating*
After some quick math and a few tears, I found that there are 21 terms in this series.
Now, let's find the sum using the formula for the sum of an arithmetic series, which is Sn = (n/2)[2a + (n - 1)d].
Plugging in the values, we have Sn = (21/2)[2(23) + (21 - 1)(-5)].
Now, let's solve that equation and bring on the funny results!
*Calculating*
Drumroll, please...
The answer is option C) -649. Just keep a close eye on those negative signs, they can sneak up on you!
To find the sum of a series with a common difference, you can use the formula for the sum of an arithmetic series:
Sn = (n/2) * (2a + (n-1)d)
where:
Sn is the sum of the series
n is the number of terms in the series
a is the first term of the series
d is the common difference between the terms
In the given series, we know the first term (a = 23), the common difference (d = -5), and the last term (-82). We need to find the number of terms in order to calculate the sum.
To find the number of terms, we can use the formula for the nth term of an arithmetic series:
an = a + (n-1)d
For the given series, we have:
an = -82
a = 23
d = -5
Plugging these values into the formula, we get:
-82 = 23 + (n-1)(-5)
Simplifying the equation, we have:
-82 = 23 - 5n + 5
Combining like terms, we get:
-82 = 28 - 5n
Rearranging the equation, we have:
5n = 110
Dividing both sides by 5, we get:
n = 22
Now that we know the number of terms (n = 22), we can calculate the sum using the formula for the sum of an arithmetic series:
Sn = (n/2) * (2a + (n-1)d)
Plugging in the values from the given series, we have:
Sn = (22/2) * (2(23) + (22-1)(-5))
= 11 * (46 + 21*(-5))
= 11 * (46 - 105)
= 11 * (-59)
= -649
Therefore, the sum of the series 23 + 18 + 13 + . . .+ (-82) is -649.
So, the correct option is C) -649.