232k views
2 votes
Please help me find the first 5 terms for each sequence. I also need help determining which sequences are arithmetic, geometric, or neither!

Please help me find the first 5 terms for each sequence. I also need help determining-example-1

1 Answer

3 votes

a) The first 5 terms: 7, 4, 1, -2, -5

The sequence has a common difference. Hence, it is arithmetic sequence

b) The first 5 terms: 2, 5, 9, 17, 33

it is neither

c) The first 5 terms: 3, 30, 300, 3000, 30000

it is a geometric sequence

Step-by-step explanation:

a) a(1) = 7

a(n) = a(n-1) -3 for n is greater than or equal to 2

when n= 2

a(2) = a(2-1) - 3

a(2) = a(1) - 3 = 7 - 3

a(2) = 4

a(3) = a(3-1) - 3

a(3) = a(2) - 3 = 4 - 3

a(3) = 1

a(4) = a(4-1) - 3

a(4) = a(3) - 3 = 1 - 3

a(4) = -2

a(5) = a(5-1) - 3

a(5) = a(4) - 3 = -2 - 3

a(5) = -5

The first 5 terms: 7, 4, 1, -2, -5

The difference between the terms = 4-7 = 1-4 = -3

The sequence has a common difference. Hence, it is arithmetic sequence

b) b(n) = 2*b(n-1) - 1 for n is greater than or equal to 2

b(1) = 2

b(2) = 2×b(2-1) - 1

b(2) = 2×b(1) - 1 = 2(2)-1

b(2) = 5

b(3) = 2×b(3-1) - 1

b(3) = 2×b(2) - 1 = 2(5) - 1 = 10-1

b(3) = 9

b(4) = 2×b(4-1) - 1 = 2×b(3) - 1 = 2(9) - 1

b(4) = 17

b(5) = 2×b(5-1) - 1 = 2×b(4) - 1 = 2(17) - 1

b(5) = 33

The first 5 terms: 2, 5, 9, 17, 33

The difference between the terms = 5-2 = 3, 9-5 =4, 17 - 9 = 8

The difference are not the same. Hence, no common difference (not an arithmetic sequence)

we find the common ratio:

5/2 = 2.5, 9/5 = 1.8, 17/9 = 1.89

No common ratio (not a geometric sequence)

Hence, it is neither

c) c(n) = 10×c(n-1) for n is greater than or equal to 2

c(1) = 3

c(2) = 10×c(2-1) = 10×c(1) = 10 × 3

c(2) = 30

c(3) = 10 ×c(3-1) = 10×c(2) = 10 ×30

c(3) = 300

c(4) = 10 ×c(4-1) = 10×c(3) = 10 ×300

c(4) = 3000

c(5) = 10 ×c(5-1) = 10×c(4) = 10 ×3000

c(5) = 30000

The first 5 terms: 3, 30, 300, 3000, 30000

The difference between the terms = 300 -30 = 290, 3000-300= 2700

The difference are not the same. Hence, no common difference (not an arithmetic sequence)

We find the common ratio:

30/3 = 10, 300/30 = 10, 3000/300 = 10

The common ratio are the same.

Hence, it is a geometric sequence

User Eddiem
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories