Question

2/3, 10/19, 26/51, 50/99, 82/163,? ​

Answer 1

Step-by-step explanation:

2/3, 10/19, 26/51, 50/99, 82/163,?

2/3, 10/19, 26/51, 50/99, 82/163,?

Answer 2

The given question is

$\frac{2}{3} \frac{10}{19} \frac{26}{51} \frac{50}{99} \frac{82}{163} x$

Here in this question, we have to find the value of x.

let us find out what logic the sequence works.

The logic followed on numerator and denominator is different.

let's see what logic is followed here.

consider all the numerators

$2 \: \: 10 \: \: 26 \: \: 50 \: \: 82$

$2 + 8 = 10 \\ 10 + 2(8) = 10 + 16 = 26 \\ 26 + 3(8) = 26 + 24 = 50 \\ 50 + 4(8) = 50 + 32 = 82$

The same logic has been used for the next term, applying the concept we get the value as

$82 + 5(8) = 82 + 40 = 122$

The logic used in the numerator is

a1+n(8)=a2.

Now, let us consider the denominator the logic used in the denominator is

$3 \: 19 \: \: 51 \: \: 99 \: \: 163$

let us find the logic in between them.

$3 + 1(16) = 19 \\ 19 + 2(16) = 19 + 32 = 51 \\ 51 + 3(16) = 51 + 48 = 99 \\ 99 + 4(16) = 99 + 64 = 163$

using the same, we find the next term as

$163 + 5(16) = 163 + 80 = 243$

the logic used in the denominator is

a1+n(16)=a2.

Therefore, the final answer will be

$\frac{2}{3} \frac{10}{19} \frac{26}{51} \frac{50}{99} \frac{82}{163} \frac{122}{243}$

The above-given sequence is the final sequence. Therefore, the final answer to the given question is 122/243

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