2.1 Change in arithmetic and geometric sequences
What is the difference between a sequence and a function in terms of their graphs?
What is the common characteristic of successive terms in an arithmetic sequence?
Write the general term of an arithmetic sequence with a common difference d.
What is the common characteristic of successive terms in a geometric sequence?
Write the general term of a geometric sequence with a common ratio r.
Given an arithmetic sequence with a first term of 5 and a common difference of 3, find the 10th term.
Given a geometric sequence with a first term of 2 and a common ratio of 3, find the 7th term.
An arithmetic sequence starts with a first term of 4 and has a common difference of 2. Write the first five terms of this sequence.
A geometric sequence starts with a first term of 3 and has a common ratio of 2. Write the first five terms of this sequence.
Given a sequence denoted by a_n, where a_n = 2n + 1. Is this sequence arithmetic or geometric? Justify your answer.
Given a sequence denoted by g_n, where g_n = 2^n. Is this sequence arithmetic or geometric? Justify your answer.
Consider an arithmetic sequence where the 5th term is 8 and the 10th term is 18. Find the common difference.
Consider a geometric sequence where the 2nd term is 4 and the 4th term is 16. Find the common ratio.
Consider the first three terms of the arithmetic sequence: 2,\,-1,\,-4,\,7,\, \ldots
Find d, the common difference.
State the expression for finding T_n.
Determine T_{10}.
Consider the first four terms of the following geometric sequences:
Evaluate \dfrac{T_2}{T_1}.
Evaluate \dfrac{T_3}{T_2}.
Evaluate \dfrac{T_4}{T_3}.
Hence, find T_5.
3,\,6,\,12,\,24,\,\ldots
−2,\,4,\,−8,\,16,\, \ldots
0.5,\,1,\,2,\,4,\, \ldots
\dfrac{1}{3},\,\dfrac{1}{9},\,\dfrac{1}{27},\,\dfrac{1}{81},\, \ldots
Consider an arithmetic sequence with a common difference of 3. If the sum of the first 20 terms is 610, what is the first term of the sequence?
Consider a geometric sequence with a common ratio of 2. If the sum of the first 10 terms is 1022, what is the first term of the sequence?
How does the rate of change in the terms of an increasing arithmetic sequence compare to that of an increasing geometric sequence?