Help with sequences?

Question

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Answer 1

The series

The formula for finding nth terms is

Formula for sumof nth term is

Substitute

Answer 2

25)

The geometric sequence

The formula for finding nth terms is

Find common ratio.

Find next three terms.

Substitute

The next three terms are

Answer 3

26)

The geometric sequence

The formula for finding nth terms is

Find common ratio.

Find next three terms.

Substitute

The next three terms are

Answer 4

27)

Three geometric means between

Find the three geometric sequence.

Consider

Here,

The formula for finding nth terms is

Find common ratio.

Substitute

Find three geometric terms.

Substitute

Three geometric terms are