Question

If the sum of first 10 terms is 33 times the sum of first five terms of a gp find the common ratio

Answer 1

10 +33x = 5

33x=5-10

x= -5/33

Answer 2

The common ratio is 2.

Step-by-step explanation:

Consider the provided information.

The sum of GP can be calculated as: $S_n=\dfrac{a(r^n-1)}{r-1}$

It is given that  the sum of first 10 terms is 33 times the sum of first five terms of a gp.

We need to find the value of r.

Substitute the respective values in the above formula.

$\dfrac{a(r^{10}-1)}{r-1}=33\times\dfrac{a(r^{5}-1)}{r-1}$

$(r^{10}-1)=33(r^{5}-1)$

Substitute $r^5=b$ in above formula.

$(b^{2}-1)=33(b-1)$

$\dfrac{(b^{2}-1)}{b-1}=33$

$b+1=33$

$b=32$

Substitute the value of b.

$r^5=32$

$r=2$

Hence, the common ratio is 2.

#Learn more

THE SUM OF FIRST 20 TERMS OF A G.P. IS 244 TIMES THE SUM OF ITS FIRST 10 TERMS. the comman ratio is?

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