<span>
This arithmetic sequence has a common difference of 4, meaning that we add 4 to a term in order to get the next term in the sequence.
The recursive formula for an arithmetic sequence is written in the form
For our particular sequence, since the common difference (d) is 4, we would write
So once you know the common difference in an arithmetic sequence you can write the recursive form for that sequence.
However, the recursive formula can become difficult to work with if we want to find the 50th term. Using the recursive formula, we would have to know the first 49 terms in order to find the 50th. This sounds like a lot of work. There must be an easier way. And there is!
Rather than write a recursive formula, we can write an explicit formula. The explicit formula is also sometimes called the closed form. To write the explicit or closed form of an arithmetic sequence, we use
<span><span>an</span> is the nth term of the sequence. When writing the general expression
for an arithmetic sequence, you will not actually find a value for
this. It will be part of your formula much in the same way x’s and y’s
are part of algebraic equations.
a1
is the first term in the sequence. To find the explicit formula, you
will need to be given (or use computations to find out) the first term
and use that value in the formula.
n is treated like the variable in a sequence. For example, when writing the general explicit formula, n is the variable and does not take on a value. But if you want to find the 12th term, then n does take on a value and it would be 12.
d is the common difference
for the arithmetic sequence. You will either be given this value or be
given enough information to compute it. You must substitute a value for d
into the formula. </span> You must also simplify your formula as much as possible. </span>
Answer:
4. 14.03 miles
5. 15.02 kilometers
6. 19.95 meters
Step-by-step explanation:
4. We need to use the law of sines, which states that for a triangle with angles A, B, and C and sides a, b, and c, respectively, then:
Here, a = 30, <A = 130, and <B = 21. So, let's plug these in:
b = AC = 
≈ 14.03 miles
5. Here, c = 7, <C = 23, and <A = 123. We want to find BC, which is just a:
a = BC = 
≈ 15.02 kilometers
6. Here, c = 22, <C = 88, and <B = 65. We want to find AC, which is just b:
b = AC = 
≈ 19.95 meters
Hope this helps!
-4x > 16
Divide -4 on both sides. Don't forget to flip sign since we are dividing by a negative number.
x < -4
Answer:
19.4 units
Step-by-step explanation:
if perimeter is 2p+2w then the equation is
(2x6.2)+(2x3.5)
12.4+7
19.4 units
hope this helps have a blessed day :)
Answer:
x = -1 ; y = 1
Step-by-step explanation:
x = -1
y = 1
Plug in the corresponding numbers to the corresponding variables:
y < -x + 1
(1) < -(-1) + 1
1 < 1 + 1
1 < 2 (True)
y > x
1 > -1 (True).
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