Arithmetic sequence
Geometric
Partition
Riddles
Facts
100
Tell whether if the sequence is arithmetic or not. Explain why or why not.
-1,-3,-5,-7
Sequence A is an arithmetic sequence since every pair of consecutive terms has a common difference of -2, that is, d=-2
100
Is this a geometric sequence
t0 = 4
tn = tn-1 x 3
Answer: Yes!
Why? :
A geometric sequence is one in which the next term is found by multiplying the previous term by a particular constant. Thus, we look for an implicit definition that involves the multiplication of the previous term.
100
How many partitions are there for the number 5
Answer: p(5) = 7
1. 5
2. 4 + 1
3. 3 + 2
4. 3 + 1+ 1
5. 2 +2 + 1
6. 2 + 1 + 1 +1
7. 1 +1 +1 +1 +1
100
If there are 4 apples and you take away 3, how many do you have?
Answer: Three apples( because you're the one who took the Apples!!)
100
What was Srinivasa Ramanujan's death caused by?
Answer: Death was caused by Tubercolisis
200
If a sequence has a first term of a1= 12 and a common difference d=-7 Write the formula that describes this sequence. Use the formula of the arithmetic sequence.
an= a1 + (n-1)d
an = 12 + (n-1) -7
an= 12 -7n + 7
an= -7n + 19 (answer)
200
what is the explict formula for the below sequence finding the 20th value
-1,2,-4,8,-16,32
geometric formula: an = a1 x rn-1
r= -2 and a1= -1
an = (-1) x (-2)n-1
a20 = (-1) x (-2)20-1
a20 = 524,288 (answer)
200
What is the partition of 7?
Answer: p(7)= 15
7, 6+1, 5+2, 5+1+1, 4+3, 4+2+1, 4+1+1+1, 3+3+1, 3+2+2, 3+2+1+1, 3+1+1+1+1, 2+2+2+1, 2+2+1+1+1, 2+1+1+1+1+1, 1+1+1+1+1+1+1.
200
If eggs are $0.12 a dozen, how many eggs can you get for a dollar?
Answer: 100 eggs, at one penny each
200
What was the book called that Srinivasa was introduced to in his mid-teens?
Answer: A ¨Synopsis of Elementary Results in Pure and Applied Mathmatics¨
300
Write the formula describing the sequence 6,14,22,30,...
The first term is 6, which means a1= 6 The common difference is d=8
14-6 = +8(=d)
an= a1 + (n-1) d
an= 6 + (n-1) 8
an= 8n -2 (answer)
300
Find the 10 th term of a geometric sequence if a1 = 45 and the common ration r = 0.2.
an = a1 x rn-1
a10= 45 x 0.210-1 = 2.304 x 10-5 (answer)
300
What number consist of this partition?
4 +2 + 1 +1 +1
Answer: P(n), n=9
4 + 2 = 6
6 + 3 = 9
300
What is the next number in the series? 7,645 5,764 4,576
Answer: 6,457 because the last number is moved to the front to make the next number in the series.
300
What did Srinivasa do his first paper on thst was a 17 page paper?
Answer: His first paper was on Bernoulli numbers
400
The first term of an arithmetic sequence is equal to 6 and the common difference is equal to 3. Find a formula for the n th term and the value of the 50 th term
an = a1 + (n-1)d
an= 6 + (n-1)3
an= 6 + 3n -3
an= 3n + 3 a50= 3(50) + 3
a50 = 153 (answer)
400
Identify the 10th term in the series
1/4, 1/8, 1/16, 1/32,...
Answer: 1/2048
r= 1/2
an = a1 x rn-1
a10 = 1/4 x 1/29
a10= 1/2048
400
Which number does this partition belong to?
5 + 4 + 2 +1
Answer: p(n)= P(12)
400
If it took 6 people 9 hours to build a barn, how long would it take 12 people to build the same barn?
Answer: None, because the barn is already built.
400
What was one of the three historical events that happened during Srinivasa time period?
Answer:
1. World War 1
2. Non- Cooperation Movement
3. Influenza( sickness)
500
The first term of an arithmetic sequence is equal to 200 and the common difference is equal to -10. Find the value of the 20 th term
an= a1 + (n-1)d
a20 = 200 + (20 - 1 ) -10
a20= 10 (answer)
500
Find the 15th term of the following series
120, 60, 30, 15, 7.5
r= 1/2
a15= 120 x (1/2)14
a15= .0073 (Answer)
500
How many partitions does the number 10 have?
P(10)=
Answer: P(10) = 42
500
Using only addition, add eight 8s to get the number 1,000.
Answer: 888 + 88 + 8 + 8 + 8 = 1,000.
This is the kind of number riddle you can work out with times tables, or by simple logic. First, get as close to 1,000 as you can (888). From there, it’s easy to figure out the rest.
500
What was the college that Srinivasa attended in 1906?
Answer: He attended Pachaiyappas College