Question

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Consider the series 1/4+3/2+11/4+4+21/4+....

Does the series converge or diverge?

Select answers from the drop-down menus to correctly complete the statements.

The series _____ (diverges or converges). You Consider conclude this because the series is _________ (Arithmetic, Geometric and the absolute value of the common ratio is greater than 1, Geometric and the absolute value of the common ratio is less than 1, neither arithmetic nor geometric)

Answer 1

The series diverges. You Consider concluding this because the series is in arithmetic progression.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

$a_n = a_1 + (n-1)d$

where d is the difference and a₁ is the first term of the sequence.

The given series of numbers 1/4+3/2+11/4+4+21/4+.... is an arithmetic series because the difference between any two consecutive terms is 5/4. Therefore, the blanks can be filled as,

The series diverges. You Consider conclude this because the series is in arithmetic progression.

Learn more about the Arithmetic sequence:

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