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.
[tex]a_2=2\times 4-1=8-1=7[/tex]
[tex]a_3=7\times 4-2=28-2=26[/tex]
[tex]a_4=26\times 4-3=104-3=101[/tex]
[tex]a_5=101\times 4-4=404-4=400[/tex]
So, the nh term of the sequence is
[tex]a_n=a_(n-1)\times 4-(n-1)[/tex]
Substitute n=6,
[tex]a_n=a_(6-1)\times 4-(6-1)[/tex]
[tex]a_n=a_(5)\times 4-5[/tex]
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.
[tex]a_6=400\times 4-5=1600-5=1595[/tex].
Therefore, the missing term is 1595.
