<span>Six equilateral triangles are connected to create a regular hexagon. The area of the hexagon is 24a2 – 18 square units. Which is an equivalent expression for the area of the hexagon based on the...
Answer: </span> 6(4a2 - 3)
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Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}
iren [92.7K]
Answer:
A) a_n = 5n + 2
B) a_n = (2^(n + 1)) - 1
Step-by-step explanation:
A) The sequence is given as;
{7,12,17,22,27,...}
The differences are:
5,5,5,5.
This is an arithmetic sequence following the formula;
a_n = a_1 + (n - 1)d
d is 5
Thus;
a_n = a_1 + (n - 1)5
Now, a_1 = 7. Thus;
a_n = 7 + 5n - 5
a_n = 5n + 2
B) The sequence is given as;
{ 3,7,15,31,63,...}
Now, let's write out the differences of this sequence:
Differences are:
4, 8, 16, 32
This shows that it is a geometric sequence with a common ratio of 2.
In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15
Thus, a_2 = 2a_1 + 1
Also, a_(2 + 1) = 2a_2 + 1
Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1
Thus; a_n can be expressed as:
a_n = (2^(n + 1)) - 1
Answer:
16, -16, 14, and -14
Step-by-step explanation:
The easiest way of solving this question is by setting up an equation. Let's use "n" to represent any random possible integer.
n (n + 2) = 224
Simplifying:
x^2 + 2n - 224 = 0
(n + 16)(n - 14) = 0
n = -16, 16 or n = -14, 14
<u>Check:</u>
16 * 14 = 224
-16 * -14 = 224
Thus, answers of 16, -16, 14, and -14 all work correctly.
Hey There!
3×9=27
27-15=12
Teresa has 12 pieces of Chocolate left
Hope This Helps!!!!
