Archive for February, 2015

Problem 598

 

Which of the following graphs represents a vertical shift down 1 of the parent graph of  f(x) = sinx?

 

Solution:-

598

 

Problem 597

Which of the graphs represents a vertical shift up 1 of the parent graph of f(x)= sinx ?

 

Solution:-

 

sin

 

Problem 596

Find the sum of the sequence you created in problem.Divide the sum by 11. What do you notice?

2, 3 ,5 8, 13, 21, 34, 55, 89, 144

 

Solution

 

The sum of the Fibonacci sequence in problem  = 374
Divide by 11 the sum = 374/11 = 34
We are notice the middle term of the number is remove.

 

Problem 595

Find the 5th term of the sequence in which t1 = 8 and tn = -3tn-1.

 

 Solution:-

 

t1 = 8

t2 = -3(t1) = -3(8) =-24

r = -3

a5 =  8*(-3)^{4}

a5 = 648

 

Problem 594

Find the four geometric means between 4 and 972

 

Solution:-

 

4r^{5} = 972

r^{5}  = 243

r = 3

So the  four geometric means are 12, 36, 108 and 324.

Problem 593

What are the next three terms of the following sequence?
-2, 4, -8, 16

 

Solution:-

 

a1 = -2, and r = -2

an = a1* a^{n-1}

So the next three terms -32, 64, -128

Problem 592

What are the next three terms of the following sequence?
8, 40, 200, 1000

 

Solution:-

 

a1 = 8, and r = 5

an = a1* a^{n-1}

So the next three terms 5000, 25000, 125000

Problem 591

Find S20 for the series -1 + -3 + -5 + -7 +…

 

Solution:-

 

a1 = -1, d = -2

S20 = \frac{n}{2} [2*a1 + (n-1)*d]

S20 = \frac{20}{2}  [2*(-1) + (20-1)*-2]

S20 = – 400

Problem 590

Find S10 for the series 2 + 7 + 12 + 17 +…

 

Solution:-

 

a1 = 2, d = 5

S10 = \frac{n}{2}[2*a1 + (n-1)*d]

S10 = \frac{10}{2} [2*2 + (10-1)*5]

S10 = 245

Problem 589

 

Find the 10th term of an arithmetic sequence if t1 = 2.1 and t4 = 1.83.

 

Solution:-

 

1.83 = 2.1+(4-1)d

d = -0.09

n10th = 2.1+(10-1)*(-0.09)

n10th = 1.29