The next three numbers in sequence are 22, 32 and 44
Solution:
Given sequence is:
2, 4, 8, 14, ...
We have to find the next 3 numbers in sequence
Let us understand the logic used in this sequence
[tex]First\ term = 1^2 -1+2 = 1 + 1 = 2\\\\Second\ term = 2^2 -2 + 2 = 4\\\\Third\ term = 3^2 - 3 + 2 = 9 - 1 = 8\\\\Fourth\ term = 4^2 -4 + 2 = 16-2 = 14[/tex]
Thus the formula used is:
[tex]a_n = n^2 - n +2[/tex]
Where, "n" is the location of term in sequence
To find the next three terms:
[tex]Fifth\ term = 5^2 - 5 + 2 = 25 - 3 = 22\\\\Sixth\ term = 6^2 - 6 + 2 = 36 - 4 = 32\\\\Seventh\ term = 7^2 -7 + 2 = 49 - 5 = 44[/tex]
Thus the next three numbers in sequence are 22, 32 and 44
