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Find the expression of the number sequence; 4,6,12,19

User Alpine
by
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1 Answer

6 votes

Explanation:

I think you made a typo.

this should be

4, 7, 12, 19

the differences between the terms are then

3, 5, 7

so, the next difference should be 9, and then 11 and so forth.

that means we are adding 2 more (not just 2) every time we create a new term.

a1 = 4

a2 = a1 + 3 = 7

a3 = a2 + (a2 - a1) + 2 = a1 + 3 + (a1 + 3 - a1) + 2 =

= a1 + 2×3 + 1×2 = a1 + 4×2 = 12

a4 = a3 + (a3 - a2) + 2 =

= (a2 + (a2 - a1) + 2) + (a2 + (a2 - a1) + 2 - a2) + 2 =

= (a1 + 3 + (a1 + 3 - a1) + 2) + (a1 + 3 + (a1 + 3 - a1) + 2 - a1 - 3) + 2 =

= (a1 + 2×3 + 2) + 1×3 + 2 + 2 =

= a1 + 3×3 + 3×2 = a1 + 5×3 = 19

this tells us

an = a1 + (n+1)(n-1) = 4 + n² - 1 = n² + 3

f(n) = n² + 3

User Alexpfx
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7.7k points