Question

Select the option for "?" that continues the pattern in each question. 2, 7, 26, 101, 400, ?

Answer 1

Answer:

1595

Step-by-step explanation:

The given sequence is

2, 7, 26, 101, 400, ?

We need to find the missing term in this pattern.

First term is 2.

$a_2=2\times 4-1=8-1=7$

$a_3=7\times 4-2=28-2=26$

$a_4=26\times 4-3=104-3=101$

$a_5=101\times 4-4=404-4=400$

So, the nh term of the sequence is

$a_n=a_(n-1)\times 4-(n-1)$

Substitute n=6,

$a_n=a_(6-1)\times 4-(6-1)$

$a_n=a_(5)\times 4-5$

To find the next term, we need to find the product of 400 and 4 and after that the difference of resultant number and 5.

$a_6=400\times 4-5=1600-5=1595$.

Therefore, the missing term is 1595.