Show that the sequence {an}is a solution of the recurrence relation an = an−1 + 2an−2 + 2n − 9 if a) an = −n + 2.&nbsp;

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Show that the sequence {an}is a solution of the recurrence relation an = an−1 + 2an−2 + 2n − 9 if a) an = −n + 2.&amp;nbsp;

Eliza Beth13 · Accepted Answer

To show that the sequence {an} is a solution of the recurrence relation an=an−1+2an−2+2n−9 with an=−n+2, we need to substitute the given value of an into the recurrence relation and verify that it holds true.Let&#039;s substitute an=−n+2 into the recurrence relation:−n+2=(−n+1)+2(−n+2)+2n−9Now, let&#039;s simplify the equation:−n+2=−n+1−2n+4+2n−9Simplifying further:−n+2=−n−4+1−9Combining like terms:−n+2=−n−12We can see that both sides of the equation are equal. Therefore, the sequence {an} with an=−n+2 is indeed a solution of the given recurrence relation an=an−1+2an−2+2n−9.This demonstrates that the sequence {an}, defined as an=−n+2, satisfies the given recurrence relation.

Show that the sequence {an}is a solution of

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