what is the nth term for this sequence 4 13 28 49 76

Question

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Answer 1

Write out the terms, their differences and their 2nd differences.

4      13      28      49      76

    9       15       21      27

         6        6         6

Since it is the 2nd differences that are equal, then the nth term of the sequence is given by a 2nd degree polynomial.

tn = an^2 + bn + c, where t1 = 4, t2 = 13, t3 = 28, ...

n = 1:   4 = a + b + c   -------------------- (1)

n = 2:  13 = 4a + 2b + c  ----------------- (2)

n = 3:  28 = 9a + 3b + c   ----------------- (3)

Subtracting (1) from (2) and (2) from (3),

 9 = 3a + b  ------ (4)

15 = 5a + b  ----- (5)

Subtract (4) from (5).

6 = 2a

a = 3

b = 0

c = 1

Expression for the nth term is: tn = 3n^2 + 1

Answer 2

3n^2 + 0n + 1

Answer 3

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