Question

2,2,6,10,12,30,20,68,?​

Answer 1

Answer:

$a=2$

$d=t_2-t_1=t_3-t_2$

$d=2-1=6-2\\d=1 \neq 4$

∴It is not an AP

Answer 2

Given:

A series 2,2,6,10,12,30,20,68,?​.

To find:

The next term after 68.

Solution:

In the given series, the number at an even place follows a different pattern than the number at an odd place.

Take the numbers of even place, 2,10,30,68,...

Here the difference between the above-mentioned pattern is,

$2^3+2=8+2\\=10\\3^3+3=27+3\\=30\\4^3+4=64+4\\=68$

Take the numbers of an odd place, 2,6,12,20,...

Here the difference between the above-mentioned pattern is,

$2+2\times1=2+2\\=4\\2+2\times2=2+4\\=6\\2+2\times3=2+6\\=8$

So, the gap between 20 and its next term placed after 68 will be,

$2+2\times4=2+8\\=10$

And the term is,

$10+20=30$

Thus, the number that will come in the place of the question mark is 30.