## 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*

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*

So the next three terms 5000, 25000, 125000

## Problem 591

Find S_{20} for the series -1 + -3 + -5 + -7 +…

**Solution:-**

a1 = -1, d = -2

S_{20} = [2*a1 + (n-1)*d]

S_{20} = [2*(-1) + (20-1)*-2]

S_{20} = – 400

## Problem 589

Find the 10th term of an arithmetic sequence if t_{1} = 2.1 and t_{4} = 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 S_{20} for the arithmetic series 8 + 16 + 24 + 32 +…

**Solution:-**

a1 = 8, d =8

S_{20} = n/2[2*a1 + (n-1)*d]

S_{20} = 20/2[2*8 + (20-1)*8]

S_{20} = 1680