Write an equation for the nth term of the geometric sequence 6. - 54, 486,

Given:

The geometric sequence is:

To find:

The equation for the nth term of the given geometric sequence.

Solution:

We have the given geometric sequence,

Here, the first term is 6 and the common ratio is:

The nth term of a geometric sequence is:

Where, a is first term and r is the common ratio.

Putting in the above formula, we get

Therefore, the equation for the nth term of the given geometric sequence is .

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

345

step-by-step explanation: