Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 1 - From Patterns to Generalizations: Sequences and Series>Chapter review>Q 1

MEDIUM

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IMPORTANT

Earn 100

For the sequence of the consecutive multiples of $5$ greater than $104, u_{7}, S_{9}$ . $(a)$ identify whether the sequence is arithmetic, geometric or neither. $(b)$ If it is arithmetic or geometric, find an expression of $u_{n}$ . $(c)$ If it is arithmetic or geometric, find the indicated term. $(d)$ If it is arithmetic or geometric, find the indicated sum.

Important Questions on From Patterns to Generalizations: Sequences and Series

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 1 - From Patterns to Generalizations: Sequences and Series>Chapter review>Q 2

In an arithmetic sequence,

u_{6} = - 5 and u_{9} = - 20

. Find

S_{20}

.

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 1 - From Patterns to Generalizations: Sequences and Series>Chapter review>Q 3

Write down the first five terms for the recursive sequence

u_{n} = - 2 u_{n - 1} + 3 with u_{1} = - 4

.

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 1 - From Patterns to Generalizations: Sequences and Series>Chapter review>Q 4

For the geometric series

0.5 - 0.1 + 0.02 . . . ., S_{n} = 0.416

. Find the number of terms in the series.

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 1 - From Patterns to Generalizations: Sequences and Series>Chapter review>Q 5

For a geometric progression,

u_{3} = 4.5 and u_{7} = 22.78125

. Find the value of the common ratio and the first term.

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 1 - From Patterns to Generalizations: Sequences and Series>Chapter review>Q 6

Which of the following sequences has an infinite sum Justify your choice and find that sum.

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 1 - From Patterns to Generalizations: Sequences and Series>Chapter review>Q 7

How many terms are in the sequence

4, 7, 10, . . . ., 61

?

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 1 - From Patterns to Generalizations: Sequences and Series>Chapter review>Q 8

In a geometric sequence, the fourth term is

8

times the first term. If the sum of the first

8

terms is

765

, find the

9 th

term of the sequence.

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 1 - From Patterns to Generalizations: Sequences and Series>Chapter review>Q 9

Three consecutive terms of a geometric sequence are

x - 3, 6 and x + 2

. Find all the possible values of

x

.