To find explicit formulas, you need two things. The common difference and the first term.
For example, #18
The first term = -15
The common difference = -20 -(-15) = -20 + 15 = -5
y = A + B(n - 1)
A = our first term
B = our common difference
n = the term you want to find in the sequence.
Leta plug our numbers in from #18
y = -15 + -5(n - 1)
Let's find the 4th term in the sequence.
y = -15 + -5(4 - 1)
y = -15 + -5(3)
y = -15 + -15
y = -30
Either or can be used with any triangle...I personally find the law of sines is often more compact as in this case we can just say;
(sin115)/18=(sin40)/c (with no need for b or B as would be needed with the law of cosines...)
c=18(sin40)/(sin115)
c≈12.77
Given that the First term of the Arithmetic sequence = -3
⇒ a = -3
We know that nth term of a Arithmetic sequence is : Tn = a + (n - 1)d
where a is the first term and d is the common difference
Given that 10th term is 15
⇒ T₁₀ = -3 + (10 - 1)d
⇒ -3 + (10 - 1)d = 15
⇒ 9d = 18
⇒ d = 2
⇒ Common difference of given Arithmetic Sequence is 2
Total number of cards = 25 .
Total number of possible draws = 25
Number of possible successes = 5
(The successful draws are 1, 2, 3, 9, and 18.)
Probability of success = 5/25 = <em>1/5 </em> = 0.2 = 20%
