USE SUMMATION NOTATION TO WRITE A ARITHMETIC SERIES FOR THE FOLLOWING MUMBER OF TERMS.
10+7+4+...;N=6
To write an arithmetic series using summation notation, we need to determine the first term, the common difference, and the number of terms. In this case, we are given the first term (10) and the number of terms (N = 6).
The common difference (d) can be found by subtracting the second term from the first term. In this case, the second term (7) minus the first term (10) gives us a common difference of -3.
To write the arithmetic series, we can use the summation notation, which is represented as:
Σ(a + d(n-1))
where:
Σ represents the sum
a represents the first term
d represents the common difference
n represents the number of terms
Plugging in the values, we get:
Σ(10 + (-3)(n-1))
Now we substitute the value of n with 6:
Σ(10 + (-3)(6-1))
Simplifying further:
Σ(10 + (-3)(5))
Σ(10 + (-15))
Final answer:
Σ(-5)