The geometric series is convergent and the value is 16.
<h3>How to illustrate the information?</h3>
Recall that the sum of an infinite geometric series, S, given first term, t_1, and common ratio, r, is given by:
S = t_1/(1 - r)
Note that:
3 = (4)(3/4)
9/4 = (3)(3/4)
27/16 = (9/4)(3/4)
So this a geometric series with t_1 = 4 and r = 3/4. Therefore:
4 + 3 + 9/4 + 27/16 + ... = 4/(1 - 3/4) = 4/(1/4) = 16
The correct option is 16.
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Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum
4+3+ 9/4 +27/16 +???
choices are
1. 3/4
2. 12
3. 4
4. divergent
5. 16
Answer:
this is so easy
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
STEP 1:
determine equations needed
x= # of $10 tickets
y= # of $14 tickets
QUANTITY EQUATION
x + y= 800
COST EQUATION
$10x + $14y= $9,040
STEP 2:
multiply quantity equation by -14
-14(x + y)= -14(800)
-14x - 14y= -11,200
STEP 3:
add new quantity equation in step 2 to cost equation of step 1 to solve for x using elimination
-14x - 14y= -11,200
10x + 14y= 9040
y term cancels out
-4x= -2160
divide both sides by -4
x= 540 ten dollar tickets
STEP 4:
substitute x value in step 3 into either original equation
x + y= 800
540 + y= 800
subtract 540 from both sides
y= 260 fourteen dollar tickets
ANSWER: There were 540 $10 tickets and 260 $14 tickets sold.
Hope this helps! :)
<span>for part (a) find the sum of the first n terms of the arithmetic series. for part (b) find n for the given sum Sn.
45. 3+8+13+18+23+...
a. n=20
b. Sn=366
46. 50+42+34+26+18+...
a. n=40
b. Sn=182
47. -10+(-5)+0+5+10+...
a. n=19
b. Sn=375
48. 34+31+28+25+22+...
a. n=32
b. Sn=-12
49. 2+9+16+23+30+...
a. n=68
b. Sn=1661
50. 2+16+30+44+58+...
a. n=24
b. Sn=2178
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