CSUS Math 1 1.2 Homework
The formula for the nth octagonal number is O subscript n=n(6n-4)/4. Use the formula to find the 19thoctagonal number.
1045
Find the seventh row of the triangle. Choose the correct answer below.
1 6 15 20 15 6 1
Find the eighth row of the triangle. Choose the correct answer below.
1 7 21 35 21 7 1
Find the ninth row of the triangle. Choose the correct answer below.
1 8 28 56 70 56 28 8 1
Use the formula S = n(n+1)/2 to find the sum of 1 + 2 + 3 + ... + 295
1+2+3+...+295=43,660
Use the formula S = n(n+1)/2 to find the sum of 1 + 2 + 3 + ... + 510
1+2+3+...+510=130,305
Use the formula S=n^2 to find the sum of 1+3+5+...=505
1+3+5+...+505=64,009
The mathematical array of numbers known as Pascal's triangle consists of rows of numbers, each of which contains one more entry than the previous row. The first six rows are arranged "flush left" to the right. Add along the blue diagonal lines. Write these sums in order from left to right. What sequence is this? Add along the blue diagonal lines. Write these sums in order from left to right.
1, 1, 2, 3, 5, 8
Use patterns to complete the table below(triangular)
1, 3, 6, 10, 15, 21,268, 36
Use patterns to complete the table below (square)
1, 4, 9, 16, 25,36, 49, 64
Use patterns to complete the table below (hexagonal)
1, 6, 15, 29, 45, 66, 91, 120
Use patterns to complete the table below (pentagonal)
1,5,12,22,36,51,70,92
Use patterns to complete the table below (heptagonal)
1,7,18,34,55,81,112,148
Use patterns to complete the table below (octagonal)
1,8,21,40,65,96,133,176
The formula for the nth hexagonal number is Hp subscript n=n(5n-3)/2. Use the formula to find the 12th heptagonal number.
342
The formula for the nth pentagonal number is P Subscript n=n(3n-1)/2. Use the formula to find the 17th pentagonal number.
425
The formula for the nth hexagonal number is H subscript n=n(4n-2)/2. Use the formula to find the 15th hexagonal number.
435
Take any four-digit number whose digits are all different. Arrange the digits in decreasing order, and then arrange them in increasing order. Now subtract. Repeat the process, called the Kaprekar routine, until the same result appears. For example, consider a number whose digits are 1, 5, 7, and 9, such as 1579. 9751 8721 7443 9963 6642 −1579 −1278 −3447 −3669 −2466 8172 7443 3996 6264 4176 7641 −1467 6174 Use the procedure described here, starting with a three-digit number of your choice whose digits are all different. You should arrive at a particular three-digit number that has the same property described for 6174. What is this three-digit number?
495
The mathematical array of numbers known as Pascal's triangle consists of rows of numbers, each of which contains one more entry than the previous row. The first six rows are shown to the right. Each row begins and ends with a 1. Discover a method whereby the other entries in a row can be determined from the entries in the row immediately above it. (Hint: See the bold entries above.) Find the next three rows of the triangle. Which of the following methods can be used to find the entries in a given row that are other than 1?
Add the two entries immediately to the left and right in the row above it.
Explain how the following diagram geometrically illustrates the formula 1+3+5+7+9=5^2
Each small square represents a unit. The first five figures represent the first five odd counting numbers, and are shaped so they can be stacked together. When these figures are stacked together, they form a square that is five units on each side, which represents 5^2
Observe the formulas Hn=n(4n-2)/2, Hpn+=n(5n-3(/2, and On=n(6n-4)/2. Use patterns and inductive reaoning to predict the formula for Nn, the nth nonagonal number. (A nonagon has nine sides). Then find the sixth nonagonal number.
Nn=n(7n-5)/2
The formula for the nth triangular number is T Subscript n=n( n+1)/2 Use the formula to find the 10th triangular number
The 10th triangular number is 55
Equations are given below illustrating a suspected number pattern. Determine what the next equation would be, and verify that it is indeed a true statement. 999,999×5=4,999,995 999,999×6=5,999,994
The next equation would be 999,999×7=6,999,993. This is a true statement because the product of 999,999 and 7 is 6,999,993.
What sequence is this? Choose the correct answer below.
This is a fibonacci sequence
Use inductive reasoning to answer. If you add two consecutive triangular numbers, what kind of figurate number do you get?
a square number
What is the sixth nonagonal number
sixth nonagonal number is 111.
