What is the 10th term of the sequence 81, 27, 9?

Question:

What is the 10th term of the sequence 81, 27, 9?

I Geometric Progression(G.P)

A Geometric progression is a sequence of numbers in which the first term is non zero and each of its succeeding terms 'r' times the previous term, where 'r' is a non-zero number and this fixed number 'r' is known as the common ratio of the G.P.

The first term of G.P. is non -zero.

The general form of a G.P. is given by

{eq}\displaystyle a ,ar, ar^2.......ar^{n-1} {/eq}

here {eq}a ={/eq} first term,{eq}r ={/eq} common ratio,{eq}n=n^{th}{/eq} term of G.P.

Formula

{eq}n^{th}~ term {/eq}of G.P. is given by

{eq}\displaystyle g_n = ar^{n-1} {/eq}

here {eq}g_n =n^{th} ~term ~of~ G.P. {/eq}

Answer and Explanation: 1

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Given

the first term of G.P. is {eq}a=81{/eq} and common ratio of G.P. is {eq}\displaystyle r=\frac{1}{3} {/eq}

{eq}n=10 {/eq}

so

{eq}\display...

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Working with Geometric Sequences

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Chapter 21 / Lesson 8
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A geometric sequence can be identified by its specific common ratio. Learn about the definition of a geometric sequence, how to find the common ratio, how to continue a geometric sequence, and explore several examples of geometric sequences.


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