Its 16.50
11.75 + 4.75
add them and you have your answer :) hope that helped
difference.
If the sum of the first 10 terms of an arithmetic sequence is 235 and the sum of the second 10 terms is 735. The first term of the arithmetic sequence is -21.5 and the common difference is 10.
Let's a represent the first term of the arithmetic sequence and the common difference as d
Formula for the sum of the first n terms of an arithmetic sequence is given by:
S_n = (n/2) * [2a + (n - 1)d]
So,
Sum of the first 10 terms: S₁₀ = 235
Sum of the second 10 terms: S₂₀ = 735
First 10 terms:
S₁₀ = (10/2) * [2a + (10 - 1)d]
235 = 5 * [2a + 9d]
47 = 2a + 9d
Second 10 terms:
S₂₀ = (10/2) * [2a + (20 - 1)d]
735 = 5 * [2a + 19d]
147 = 2a + 19d
Now we have a system of equations:
2a + 9d = 47
2a + 19d = 147
(2a + 19d) - (2a + 9d) = 147 - 47
10d = 100
d = 10
Substitute it into the first equation to solve for "a":
2a + 9(10) = 47
2a + 90 = 47
2a = -43
a = -21.5
Therefore the first term of the arithmetic sequence is -21.5 and the common difference is 10.
Learn more about arithmetic sequence here:brainly.com/question/6561461
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Answer:
Step-by-step explanation:
The sum of the first 10 terms of an arithmetic sequence is:
the sum of the second 10 terms is: a₁₁ + a₁₂+...+ a₂₀
And the sum of the first 20 terms of an arithmetic sequence is:
so the sum of the second 10 terms is:
Therefore we have:
and:
Answer:
19.2
Step-by-step explanation:
1st Case:
4 and 5 are legs of the right triangle.
Using the pythagorean therom: a^2+b^2=c^2
We can say that 4^2+5^2=x^2
16+25=x^2
41=x^2
x=√41
√41 is about 6.4
x=6.4
2nd Case
5 is the hypotenuse of the right triangle and 4 is the legs.
Using the pythagorean therom: a^2+b^2=c^2
We can say that 4^2+x^2=5^2
16+x^2=25
x^2=9
x=3
Final Step
We need to multiply the two possible lengths for x. So for case 1 the length of x was 6.4 and for case two the length was 3. 6.4*3=19.2
Anwser: 19.2