A. consider the finite arithmetic series 10+13+16+...+31. how many terms are in it? Explain.
B. evaluate the series
for your AS
a = 10
d = 3
term(n) = a+(n-1)d
so 31 = 10 + (n-1)(3)
21 = 3(n-1)
7 = n-1
n = 8
there are 8 terms
sum(8) = (8/2)(first + last)
= 4(10+31) = 164
THANK YOU!!!
16. You have a series of four chemical reactions (1--> 2 --> 3 --> 4). How do you calculate the H2 if you know the other H values?
H2 = (H1)(H3)/(H4)
H2 = H4 (H1 + H3)
H2 = H1 + H3 + H4
H2 = H1 + H3 H4
A. To find the number of terms in a finite arithmetic series, we need to determine the common difference and the first and last terms.
In this case, the first term is 10, and the last term is 31. To find the common difference, we subtract the last term from the first term: 31 - 10 = 21.
Since this is an arithmetic series, each term is obtained by adding the common difference to the previous term.
To find the number of terms, we can use the formula:
Number of terms = (Last term - First term) / Common difference + 1
Substituting the values we have, we get:
Number of terms = (31 - 10) / 21 + 1
= 21 / 21 + 1
= 1 + 1
= 2
Therefore, there are 2 terms in the given arithmetic series.
B. To evaluate the series, we can use the formula for the sum of an arithmetic series:
Sum = (Number of terms / 2) * (First term + Last term)
Substituting the values we obtained earlier:
Sum = (2/2) * (10 + 31)
= 1 * 41
= 41
Therefore, the sum of the given arithmetic series is 41.