What is the sum of the first 19 terms of the series: 63 + 55 + 47 + 39 + 31 + …?
I think it is 769.5
is it right?
No, that can't be right.
Since every term is reduced by 8 from the previous term, and you start out with an integer, the sum must be an integer. The sum will also be negative in this case. There will be more negative terms than positive terms in the first 19.
To find the sum of the first 19 terms in the series, we need to determine the pattern and then use the formula for the sum of an arithmetic series.
Looking at the given series, we can observe that each term is decreasing by 8. So, the common difference between the terms is -8.
To find the sum of the first 19 terms, we 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 first n terms, a is the first term, d is the common difference, and n is the number of terms.
In this case, a = 63, d = -8, and n = 19.
Using the formula, we substitute these values:
Sn = (19/2)(2(63) + (19-1)(-8))
Simplifying further:
Sn = (19/2)(126 - 8(18))
Sn = (19/2)(126 - 144)
Sn = (19/2)(-18)
Sn = -171
Therefore, the sum of the first 19 terms of the series is -171, not 769.5.