Question

find the last term of g.p whose first term is 9 and coman ratio is 1/3 if the sum of term of gp is 40/3

Answer 1

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Answer 2

Given:

The first term of G.P.=9

Common ratio=1/3

Sum of terms of G.P.=40/3

To find:

The last term of the G.P.

Solution:

We can find the last term by following the given process-

We know that the numbers of terms can be calculated using the sum of the G.P.

Let the number of terms be n.

The first term, a=9

The common ratio, r =1/3, is less than 1.

So,

$sum \: of \: the \: G.P.=a(1 - {r}^{n} ) \div (1 - r)$

On putting the values in the formula, we get

$40/3 = 9(1 - {(1/3)}^{n} )/1 - 1/3$

$40/3 = 9(1 - {(1/3)}^{n} ) \times 3/2$

$80 /9 = 9(1 - {(1/3)}^{n} )$

$80/81 = (1 - {(1/3)}^{n}$

${(1/3)}^{n} = 1/81$

${(1/3)}^{n} = {(1/3)}^{4}$

n=4

There are a total of 4 terms in the G.P.

The last term of the G.P.=

$a {r}^{n - 1}$

$= 9( {1/3)}^{4 - 1}$

=9/27

=1/3

Therefore, the last term of the G.P. is 1/3.