Question

The algebraic expression of a sequence is xn=n3-6n2+13n-7 is it an arithmetic sequence 3 mark question

Answer 1

-246 in algebraic expression.

Answer 2

SOLUTION

GIVEN

The algebraic expression of a sequence is

$\sf{x_n = {n}^{3} - 6 {n}^{2} + 13n - 7 }$

TO CHECK

Is it an arithmetic sequence

EVALUATION

Here the given sequence is

$\sf{x_n = {n}^{3} - 6 {n}^{2} + 13n - 7 }$

Putting n = 1 we get

$\sf{x_1 = {1}^{3} - 6 \times {1}^{2} + 13 \times 1 - 7 }$

$\sf{ \implies \: x_1 = 1 - 6 + 13 - 7}$

$\sf{ \implies \: x_1 = 1}$

Putting n = 2 we get

$\sf{x_2 = {2}^{3} - 6 \times {2}^{2} + 13 \times 2 - 7 = 8 - 24 + 26 - 7 = 3 }$

Putting n = 3 we get

$\sf{x_3 = {3}^{3} - 6 \times {3}^{2} + 13 \times 3 - 7 = 27 - 54 + 39 - 7 = 5}$

Putting n = 4 we get

$\sf{x_4 = {4}^{3} - 6 \times {4}^{2} + 13 \times 4 - 7 = 64 - 96 + 52 - 7 = 13 }$

Thus the sequence is 1 , 3 , 5 , 13 ....

So common difference does not exists

So the sequence is not arithmetic sequence

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