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10 Jul 2017, 08:20
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Going by this pattern of 3x3+1, 4x4+1, 5x5+1, 6x6+1, next numbers should be 50, 65, 82, 101 and so on.
Is this correct?
Is this correct?
12 Jul 2017, 11:59
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enzoeducation
To find any formular and to complete a sequance, those works are very impirical.
The differences between adjacent terms are 7 (=17-10), 9 (=26-17) and 11 (=37-26).
Thus the following differences could be 13, 15, 17, 19 and so on.
Rest of terms would be 50, 65, 82, 101 and so on.
How can we derive its formula?
We have following conditions.
a_1 = 10
a_n+1 = a_n + 2n +5
We can verify that a_2 = a_1 + 2*1 + 5, a_3 = a_2 + 2*2 + 5 and so on.
Then we have following equations.
a_1 = 10
a_2 = a_1 + 2*1 + 5
a_3 = a_2 + 2*2 + 5
.
.
.
a_n = a_n-1 + 2*(n-1) + 5
After making sum of all above equation, we have a_n = 2*1 + 2*2 + ... + c*(n-1) + 10 + 5*(n-1) = 2*n(n-1)/2 + 10 + 5*(n-1) = n^2 + 4n + 5 = (n+2)^2 + 1.
We have the formula of n-th term, (n+2)^2 + 1.
Happy Studying !!!
