Explicit Formula
Just in case you don't know what this is, the explicit formula is the formula that solves for any term in the series without necessarily knowing what came before the term you are solving.
<em><u>Givens</u></em>
d = t_(n + 1) - t_n You can take any term and the next term for this part of the formula
d = t_3 - t_2
t_3 = 1
t_2 = -7
d = 1 - - 7 = 8
a = -15
<em><u>Formula</u></em>
t_n = a + (n - 1)*d
t_n = -15 + (n - 1)*8
For example find the 5th term.
t_5 = - 15 + (5 - 1)*8
t_5 = - 15 + 4 *8
t_5 = -15 + 32
t_5 = 17 Which is what you have.
Recursive Formula
Computers really like this formula. They use it in what is called a subroutine and they pass values from one part of the program to a subroutine which evaluates the given and sends the result back. I'm telling you all this so you see why you are doing it. The disadvantage of it for humans is that you must know the preceding term to use the recursive formula.
<em><u>Formula</u></em>
t_n = t_(n - 1) + d
<em><u>Example</u></em>
t_6 = t_(6 - 1) + d
t_6 = t_5 + 8
t_6 = 17 + 8
t_6 = 25
You can check this by using the explicit formula.
The correct answer for this question is c
The given triangle is isosceles, so the two remaining angles in the triangle both have measure <em>xº</em>. The interior angles of any triangle sum to 180º, so that
58º + <em>xº</em> + <em>xº</em> = 180º
58 + 2<em>x</em> = 180
2<em>x</em> = 122
<em>x</em> = 61
Angles <em>y</em> and <em>z</em> are supplementary to angle <em>x</em>, so that
<em>xº</em> + <em>yº</em> = 180º
and
<em>xº</em> + <em>zº</em> = 180º
and consequently, <em>y</em> = <em>z</em>. In particular, we get
<em>y</em> = 180 - 61
<em>y</em> = 119
and so
<em>z</em> = 119
Let x = amount invested in 2% CD and y = amount invested in 3% CD
x + y = 60000
0.02x + 0.03y = 1600
SOLVE THE 1st EQUATION FOR x AND SUBSTITUTE RESULT IN 2nd
0.02(60000 - y) + 0.03y = 1600
1200 - 0.02y + 0.03y = 1600
0.03y = 400
y = 13333.34
x = 46666.66
