Question

The sum of the first three terms of an increasing G.P is 13 and their product is 27,
the sum of the first 5 terms is
10
A 125​

Answer 1

Answer:

a/r,a,ar are the terms.from product we get a=3submit in sum

so 3r^2-10r+3=0.so r=3

so the series is 1,3,9,27,81....

sum of first five terms is 121

Answer 2

The sum of five terms is 121.

Step-by-step explanation:

Consider the provided information.

Let the first three terms of an G.P are: $\dfrac{a}{r},a,ar$

The sum of 3 terms are 13.

$\dfrac{a}{r}+a+ar=13$

Their product is 27

$\dfrac{a}{r}\times a\times ar=27$

$a^3=27$

$a=3$

Substitute the value of a in $\dfrac{a}{r}+a+ar=13$

$\dfrac{3}{r}+3+3r=13$

$3r^2-10r+3=0$

$3r^2-9r-1r+3=0$

$3r(r-3)-1(r-3)=0$

$r=\frac{1}{3}\ or\ r=3$

The G.P is increasing so r=3

Now find the sum of first five terms as:

$\frac{a}{r}+a+ar+ar^2+ar^3$

Substitute the respective value as shown:

$\frac{3}{3}+3+3(3)+3(3)^2+3(3)^3=121$

Hence, the sum of five terms is 121.

#Learn more

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The sum of an infinite G.P is 5. The sum of the squares of these terms is 15. Find the G.p​