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In this lesson, we will learn how to work with sequences in recursive form.

Q1:

Find the first five terms of the sequence with general term π = π + 5 π + 1 π , where π β₯ 1 and π = β 1 3 1 .

Q2:

The π t h term in a sequence is given by π = π + π π + 2 π + 1 π . Find the first six terms of this sequence, given that π = 0 1 and π = 1 2 .

Q3:

Find the arithmetic sequence in which π = β 1 0 0 1 and π = 4 π 4 π π .

Q4:

Given that and that for , find a formula for in terms of .

Q5:

Find π + π + π 1 3 1 4 1 5 given π = β 3 1 and π = π + 5 8 π π β 1 .

Q6:

The π t h term in a sequence is given by π = π π π + 1 π . Find the first six terms of this sequence, given that π = β 1 1 8 1 .

Q7:

Find, in terms of π the general term of the sequence which satisfies the relation π = 2 2 π π + 1 π , where π β₯ 1 and π = 2 2 1 .

Q8:

The sequence π ο , where π β₯ 1 , is given by

List the next 6 terms π , β¦ , π ο§ ο§ ο§ ο¬ .

By listing the elements π , π , π , π , β¦ ο§ ο« ο― ο§ ο© , give a formula for π οͺ ο ο± ο© , in terms of π , for π β₯ 1 .

Give a formula for π οͺ ο ο± ο¨ , in terms of π , for π β₯ 1 .

Give a formula for π οͺ ο ο± ο§ , in terms of π , for π β₯ 1 .

Give a formula for π οͺ ο , in terms of π , for π β₯ 1 .

What is π ο§ ο¨ ο© οͺ ο§ ?

Solve π = 1 7 ο for π .

What is the range of the function π ο ?

Q9:

Consider the following sequence of dots.

What is the function π such that π ( π ) is the number of dots in the π th pattern?

Q10:

The graph represents the triangle wave function π ( π₯ ) , which is periodic, piecewise linear, and defined for all real numbers.

List the values of π ( 0 ) , π ( β 1 ) , and π ( 1 2 3 4 ) .

List the values of π οΌ 1 2 ο , π οΌ 3 2 ο , π οΌ 5 2 ο , and π οΌ 1 2 3 3 2 ο .

What is π οΌ β 4 9 3 3 2 ο ?

If we are given that π ( π ) is negative, what can we conclude about the number π ?

Find the equation of the line segment on which the point ( π , π ( π ) ) lies.

Hence find the value of π ( π ) correct to 3 decimal places.

Q11:

Given the sequence defined by π = π + π π₯ π + 1 π , where π = 2 7 1 and π = β 7 8 3 , find the value of π₯ .

Q12:

Find the first five terms of the sequence with general term π = π β 1 3 π + 1 π , where π β₯ 1 and π = 1 1 .

Q13:

Find the first five terms of the sequence with general term π = π β 3 π + 1 π , where π β₯ 1 and π = 1 9 1 .

Q14:

Find the first five terms of the sequence with general term π = π + 2 6 π + 1 π , where π β₯ 1 and π = 2 0 1 .

Q15:

Find the first five terms of the sequence with general term π = π + 3 π + 1 π , where π β₯ 1 and π = β 4 1 .

Q16:

The π t h term in a sequence is given by π = π + π π + 2 π + 1 π . Find the first six terms of this sequence, given that π = 9 1 and π = 1 1 1 2 .

Q17:

The π t h term in a sequence is given by π = π + π π + 2 π + 1 π . Find the first six terms of this sequence, given that π = 1 6 3 1 and π = β 1 3 0 2 .

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