91Ó°ÊÓ

The given sequence is the following.

$$\begin{gathered} 2,6,10,14,18,22,… \\ 1,8,27,64,125,216,… \\ 3,\frac{3}{4},\frac{3}{9},\frac{3}{16},\frac{3}{25},\frac{3}{36},... \\ 1,\frac{1}{3},\frac{1}{9},\frac{1}{27},\frac{1}{81},\frac{1}{243},… \\ \frac{3}{5},\frac{4}{7},\frac{5}{9},\frac{6}{11},\frac{7}{13},\frac{8}{15},… \\ \frac{3}{2},\frac{5}{5},\frac{7}{10},\frac{9}{17},\frac{11}{26},\frac{13}{37},… \end{gathered}$$

Take sequence $2,6,10,14,18,22,….$

the general form for the kth term of the sequence is,

$n=4k+2$

where k is a whole number.

So next two terms of the sequence are$26,30.$

Take sequence $1,8,27,64,125,216,…$

the general form for the kth term of the sequence is,

$n=k^3$

where k is a natural number.

So next two terms of the sequence are $343,512.$

Take sequence $3,\frac{3}{4},\frac{3}{9},\frac{3}{16},\frac{3}{25},\frac{3}{36},...$

the general form for the kth term of the sequence is,

$n=\frac{3}{k^2}$

where k is natural numbers

So next two terms of the sequence are $\frac{3}{49},\frac{3}{64}.$

Take sequence $1,\frac{1}{3},\frac{1}{9},\frac{1}{27},\frac{1}{81},\frac{1}{243},…$

the general form for the kth term of the sequence is,

$n=\frac{1}{3^k}$

where k is whole numbers.

So next two terms of the sequence are $\frac{1}{729},\frac{1}{2187}.$

Take sequence $\frac{3}{5},\frac{4}{7},\frac{5}{9},\frac{6}{11},\frac{7}{13},\frac{8}{15},…$

the general form for the kth term of the sequence is,

$n=\frac{k}{2k-1}$

where k is the natural number starting from$3.$

So next two terms of the sequence are$\frac{9}{17},\frac{10}{19}.$