Question

classify the series as arithmetic or geometric then determine whether the series is convergent or divergent

Answer 1

Convergent and Divergent Sequences and Series Practice.

1. The sequence diverges; the series diverges.
2. geometric, divergent
3. 3/5 and -1/6

Convergent and Divergent Sequences and

Series
1. 1/5 and 2/3

2.geometric, convergent

3. arithmetic, divergent

Explanation:

You’re welcome

Answer 2

Answer: Geometric , convergent

Explanation:

Given sequence is { 12 + ( -8 ) + 16/3 + ( - 32/9 ) + 64/27 + . . . . . . . }

To check whether the sequence is arithmetic , we first find difference of first two terms then find difference of third and second term .

If we get both the difference same , then it is arithmetic .

d₁ = - 8 - ( 12 ) = - 20

16 40

d₂ = ------ - ( - 8 ) = ------------

3 3

Common difference is not same , thus it is not arithmetic .

To check whether sequence is geometric , we divide second by first term and then third by second term . If we get the same ratio , then it is geometric .

-8 - 2

r₁ = ----------- = ----------

12 3

16/3 16 -2

r₂ = ---------- = ---------- = -----------

- 8 3 * ( -8) 3

Thus common ratio is same , so it is geometric .

Now we need to check whether it is convergent or divergent .

We have an infinite geometric series .

It is convergent if | r | < 1 , that is common ratio is less than 1 .

We have | r | = | - 2/3 | = | - 0.66 | = 0.66 < 1 .

Thus the geometric series converges .

Thus given series is geometric , convergent .

Third is the correct option .