Answer:
- S7 = 175
- S17 = 2465
- Sn = 1/2(n³ +n)
Step-by-step explanation:
The progression of sums is ...
1, 5, 15, 34, 65, ...
So, first differences are ...
4, 10, 19, 31
Second differences are ...
6, 9, 12, ...
Third differences are constant:
3, 3, ...
This means the expression for Sn will be a cubic expression. If dn is the first of the n-th differences, then the equation can be written as ...
Sn = S1 +(n -1)(d1 +(n -2)/2(d2 +(n -3)/3(d3)))
And this simplifies a little bit to ...
Sn = 1 +(n -1)(4 +(n -2)(n +3)/2)
In simpler form, we have ...
Sn = 1/2(n³ +n)
Then the two terms we're interested in are ...
S7 = (1/2)(7³ +7) = 175
S17 = (1/2)(17³ +17) = 2465
Answer:
<h2>Yes they are congruent by SSS criterion </h2><h3>Explanation:</h3>
AC=DC. (Given in figure)
AB=BD. (Given in figure
BC=BC. (Common)
that means triangle BAC is congruent to triangle BDC by SSS criterion
First, turn the fractions into mixed numbers.
21/4 - 27/8
Then. make the denominators the same.
4 * 2 = 8
21 * 2 = 42
42/8 - 27/8
42 - 27 = 15
15/8
15/8 = 1 7/8
Answer:
Leanne is correct. It is important that g(x) is subtracted from f(x).
Shiloh is incorrect. She subtracted f(x) from g(x), and subtraction isn't commutative.
*Just took the test, got the answer correct!! Hope this helps!
