Answer:
a. a[1] = 3; a[n] = 2a[n-1]
b. a[n] = 3·2^(n-1)
c. a[15] = 49,152
Step-by-step explanation:
Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.
The first term is 3, and the common ratio is 2.
<h3>(a)</h3>
The recursive rule is ...
a[1] = 3
a[n] = 2×a[n-1]
__
<h3>(b)</h3>
The explicit rule is ...
a[n] = a[1]×r^(n-1)
a[n] = 3×2^(n-1)
__
<h3>(c)</h3>
The 15th term is ...
a[15] = 3×2^(15-1) = 3×2^14
a[15] = 49,152
There are 20 nickels and 16 quarters
<em><u>Solution:</u></em>
Let "n" be the number of nickels
Let "q" be the number of quarters
We know that,
1 nickel = 0.05 dollar
1 quarter = 0.25 dollar
<em><u>Gabby has a bag containing 36 nickels and quarters</u></em>
Therefore,
n + q = 36
n = 36 - q ------- eqn 1
<em><u>The total value of the coins is $5</u></em>
<em><u>Thus we frame a equation as:</u></em>
number of nickels x 1 nickel + number of quarters x 1 quarter = 5
0.05n + 0.25q = 5 ------- eqn 2
<em><u>Substitute eqn 1 in eqn 2</u></em>
0.05(36 - q) + 0.25q = 5
1.8 - 0.05q + 0.25q = 5
0.2q = 3.2
q = 16
<em><u>Substitute q = 16 in eqn 1</u></em>
n = 36 - 16
n = 20
Thus there are 20 nickels and 16 quarters
Step-by-step explanation:
ans is 23 please mark me as brainlist please
<span>The diagonals of a parallelogram bisect each other.
So we just equate the two equations BE and DE
2x^2 - x = x^2 + 6
2x^2 - x - x^2 - 6 = 0
x^2 - x - 6 = 0
This is quadratic eqn. So we obtain.
(x - 3) ( x + 2) = 0
Setting each to 0 and solving for x, we have that x = 3 and x = -2
So we have two possible values for BD.
But Since BE = DE then we can simply double each
If x = 3 BD = 2 (2(3)^2 - 3) = 2 ( 18 - 3) = 30 units
If x = - 2 BD = 2((-2)^2 -3 ) = 2 (8 - 3) = 10 units</span>
.600 >
.020 > Expanded Form
<u>+ .004 </u> > <u>
</u> .624
