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Sequences Quest: Arithmetic vs Geometric

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Sequences Quest: Arithmetic vs Geometric

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Arithmetic & geometric sequences basics

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Jan Jan
Jan Jan
Philippines

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Sequences Quest: Arithmetic vs Geometric
 

Sequences Quest: Arithmetic vs GeometricOnline version

Arithmetic & geometric sequences basics

by Jan Jan
1

What is the common difference of the arithmetic sequence 7, 12, 17, 22?

2

Is the sequence 3, 9, 27, 81 arithmetic or geometric, and what is the ratio?

3

Find the 5th term of the arithmetic sequence with a1=4 and d=3.

4

Find the 4th term of the geometric sequence with a1=2 and r=-2.

5

If a1=6 and d=-2, what is a3?

6

What type of sequence has a constant ratio between consecutive terms?

7

What is the 3rd term of the arithmetic sequence with a1=5 and d=4?

8

What is the general term formula for an arithmetic sequence?

9

What is the general term formula for a geometric sequence?

10

If a1=3 and r=1/2, what is a2?

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Correct: each term increases by 5.

The ratio between terms is 3, so geometric.

a5 = 4 + (5-1)*3 = 16.

Terms: 2, -4, 8, -16; fourth term is -16.

a3 = 6 + 2(-2) = 2.

A constant ratio defines a geometric sequence.

a3 = 5 + 2*4 = 13.

Arithmetic: a_n = a1 + (n-1)d.

Geometric: a_n = a1 r^(n-1).

a2 = a1 r = 3 × 0.5 = 1.5.

 
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