Archive for the ‘Discrete Mathematics’ Category

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 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

Problem 588

 

Find S20 for the arithmetic series 8 + 16 + 24 + 32 +…

 

Solution:-

 

a1 = 8, d =8

S20 = n/2[2*a1 + (n-1)*d]

S20 = 20/2[2*8 + (20-1)*8]

S20 = 1680