Answer:
Step-by-step explanation:
The area of the metal frame is equal to the area of the square minus the area of the circle.
The area of the square is the side length squared:
The area of the circle is , with
being the radius:
Now find the area of the metal frame:
Factor out the GCF,
Factor out a
Answer:
a). 1, 3, 5, 7, 9, 11
b). 4, 6, 8, 10, 12, 14
c). 28, 30, 32, 34, 36, 38
Step-by-step explanation:
<u>Solution for question (a):</u>
<u />
The first difference of a sequence is the arithmetic sequence;
2, 4, 6, 8, 10
As clearly shown, the common difference (d) is 2.
This sequence, above, is an arithmetic sequence.
If the first term of an arithmetic sequence (AP) is 1, then the first six terms would be:
1, 3, 5, 7, 9, 11
<u>Solution for question (b):</u>
<u />
If the sum of the first two terms of an AP is ten,
Lets say the first term is x and the second term is x + 2 then;
x + (x + 2) = 10
2x = 10 - 2
x = 4
So the first term is 4 and the six terms of the AP are:
4, 6, 8, 10, 12, 14
<u>Solution for question (c):</u>
<u />
If the fifth term of an AP is 36 then,
To find the nth term in an AP we use the formula;
(where
is the nth term,
is the first term and
is the common difference).
36 = a + (5 - 1)2
36 = a + 8
a = 36 - 8 = 28
So the first term is 28 and the first terms are;
28, 30, 32, 34, 36, 38