Question

for a G.P.if t3=1/3,t6=1/81 find r​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Given,

In a G.P., t3 = 1/3

t6 = 1/81

To find,

The value of r.

Solution,

The value of r will be 1/3.

We can easily solve this problem by following the given steps.

We know that in a G.P. the ratio of the two consecutive terms is common which is called the common ratio. It is denoted by r.

According to the question,

t3 = 1/3

t6 = 1/81

We know that the formula to find the nth term in GP is given as follows:

tn = ar^(n-1)

t3 = ar^(3-1)

ar² = 1/3 --- equation (1)

t6 = ar^(6-1)

ar^5 = 1/81 ---- equation (2)

Dividing equation 2 by equation 1,

ar^5÷ar² = 1/81 ÷ 1/3

r³ = 3/81

r³ = 1/27

r³ = 1/(3)³

r³ = (1/3)³

r = 1/3

Hence, the value of r is 1/3.