MAT 100 C1-S2

The formula for the nth square number is Sn=n2. Use the formula to find the 11th square number.

The 11th square number is 121.

Use patterns to complete the table below.

Figurate Number 1st 2nd 3rd 4th 5th 6th 7th 8th Triangular 1, 3, 6, 10, 15, 21, 28, 36 Square 1, 4, 9, 16, 25, 36, 49, 64 Pentagonal, 1, 5, 12, 22, 35, 51, 70, 92 Hexagonal 1, 6, 15, 28, 45, 66, 91, 120 Heptagonal, 1, 7, 18, 34, 55, 81, 112, 148 Octagonal 1, 8, 21, 40, 65, 96, 133, 176

Use the formula S ​=n(n + 1)2 to find the sum of 1​ + 2​ + 3​ + ...​ + 810.

1​ + 2​ + 3​ + ...​ + 810 ​= 328,455

Use the method of successive differences to determine the next number in the given sequence. −4​, 1​, 13​, 32​, 58​, 91​, 131

Assuming that the pattern​ continues, the eighth term would be 178 pretty sure 7 was the constant number?

Use the method of successive differences to determine the next number in the given sequence.4​; 31​; 188​; 835​; 2672​; 6899​; 15,376

Assuming that the pattern​ continues, the eighth term would be 30,783. try x2 +29...

Use the formula for finding the sum 1+2+3+⋯+n to discover a formula for finding the sum 3+6+9+⋯+3n.

The formula for the sum 3+6+9+⋯+3n is S= 3n(n+1) over ____ 2

Several equations are given illustrating a suspected number pattern. Determine what the next equation would​ be, and verify that it is indeed a true statement. 22−12=2+1 32−22=3+2 42−32=4+3

The next equation would be 5 squared minus 4 squared equals 5 plus 452−42=5+4​, and it is a true statement.

Determine whether the sequence is an arithmetic​ sequence, a geometric​ sequence, or neither. If it is either arithmetic or​ geometric, give the next term in the sequence. 65536​, 16384​, 4096​, 1024​, 256​,...

The sequence is a geometric sequence with next term 64. Because 64x64=4096

For the following​ sequence, determine if it is an arithmetic​ sequence, a geometric​ sequence, or neither. If it is either arithmetic or​ geometric, give the next term in the sequence. 6​, 12​, 24​, 48​, 96​,..

The sequence is geometric. The next term is 6​, 12​, 24​, 48​, 96​, 192. Because 96x2 = 192

In an arithmetic​ sequence, the nth term is given by the formula an = a1 + (n-1)d where is the first term and d is the common difference.​ Similarly, in a geometric​ sequence, the nth term is given by whatever

look at the pattern of numbers. first question was to add 21 to each 26 times, second q was to x3 to each previous number 4x3=12 12x3 etc