Arithmetic and Geometric Sequences and Recurrence Relations | Questions and Answers
How can you work out the r value for a geometric sequence? Give two examples ** Answ**
2nd term/1st term or 5th term/4th term
Prove that the sum of the first n terms of an arithmetic series is S = n/2(2a + (n - 1)d) **
Answ** First write down: Ascending arithmetic sequence- S = a + (a + d) + (a + 2d) + ... + (a
+ (n - 1)d) Descending arithmetic sequence S = (a + (n - 1)d) + (a + (n - 2)d) + (a + (n - 3)d) + ...
+ a Then 2S = (2a + (n - 1)d) x n Then S = n/2(2a + (n - 1)d)
Explain what you would do if you a sequence had terms: 5, 8, 11, with the sequence representing
squares then the question said: Jacob uses a total of 948 squares in constructing the first k
patterns. Show that 3k^2 + 7k - 1896 = 0 ** Answ** Do the sequence sum equation of k =
948
A ball is dropped from a height of 80cm. After each bounce it rebounds to 70% of its precious
maximum height. Find the height to which the ball will rebound after the fifth bounce **
Answ** (0.7)^5 x 80
A ball is dropped from a height of 80cm. After each bounce it rebounds to 70% of its previous
maximum height. What do you need to use to find the total vertical distance travelled by the ball
before it stops bouncing? ** Answ** Sum to infinity
What happens when you divide by the negative here: 100(1 - 1.05^n) < -300 ** Answ** -
100(1 - 1.05^n) > 300, the sign flips
What sort of sequence is in this question: Maggie initially places £50 into an account and plans
to increase her payments by a constant amount each month. Given that she would like to reach a
total of £6000 in 29 months, by how much should Maggie increase her payment each month?
** Answ** An arithmetic sequence
Write down the notation for finding the third term a sequence ** Answ** a + 2d
How can you work out the r value for a geometric sequence? Give two examples ** Answ**
2nd term/1st term or 5th term/4th term
Prove that the sum of the first n terms of an arithmetic series is S = n/2(2a + (n - 1)d) **
Answ** First write down: Ascending arithmetic sequence- S = a + (a + d) + (a + 2d) + ... + (a
+ (n - 1)d) Descending arithmetic sequence S = (a + (n - 1)d) + (a + (n - 2)d) + (a + (n - 3)d) + ...
+ a Then 2S = (2a + (n - 1)d) x n Then S = n/2(2a + (n - 1)d)
Explain what you would do if you a sequence had terms: 5, 8, 11, with the sequence representing
squares then the question said: Jacob uses a total of 948 squares in constructing the first k
patterns. Show that 3k^2 + 7k - 1896 = 0 ** Answ** Do the sequence sum equation of k =
948
A ball is dropped from a height of 80cm. After each bounce it rebounds to 70% of its precious
maximum height. Find the height to which the ball will rebound after the fifth bounce **
Answ** (0.7)^5 x 80
A ball is dropped from a height of 80cm. After each bounce it rebounds to 70% of its previous
maximum height. What do you need to use to find the total vertical distance travelled by the ball
before it stops bouncing? ** Answ** Sum to infinity
What happens when you divide by the negative here: 100(1 - 1.05^n) < -300 ** Answ** -
100(1 - 1.05^n) > 300, the sign flips
What sort of sequence is in this question: Maggie initially places £50 into an account and plans
to increase her payments by a constant amount each month. Given that she would like to reach a
total of £6000 in 29 months, by how much should Maggie increase her payment each month?
** Answ** An arithmetic sequence
Write down the notation for finding the third term a sequence ** Answ** a + 2d
