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If
a_(1)=2,a_(2)=5 and
a_(n)=2a_(n-1)-a_(n-2) then find the value of
a_(5).
Answer:

If $a_{1}=2, a_{2}=5$ and $a_{n}=2 a_{n-1}-a_{n-2}$ then find the value of $a_{5}$ . $\newline$ Answer:

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Write and solve direct variation equations

Full solution

Q. If

a_{1}=2, a_{2}=5

and

a_{n}=2 a_{n-1}-a_{n-2}

then find the value of

a_{5}

.

\newline

Answer:

Find $a_{3}$ : Use the given recursive formula to find $a_{3}$ . The recursive formula is $a_{n}=2a_{n-1}-a_{n-2}$ . We know $a_{1}=2$ and $a_{2}=5$ . Calculate $a_{3}$ using the formula. $a_{3} = 2a_{2} - a_{1} = 2\times5 - 2 = 10 - 2 = 8$ .
Find $a_{4}$ : Use the recursive formula to find $a_{4}$ . We now know $a_{2}=5$ and $a_{3}=8$ . Calculate $a_{4}$ using the formula. $a_{4} = 2a_{3} - a_{2} = 2\times8 - 5 = 16 - 5 = 11$ .
Find $a_{5}$ : Use the recursive formula to find $a_{5}$ . We now know $a_{3}=8$ and $a_{4}=11$ . Calculate $a_{5}$ using the formula. $a_{5} = 2a_{4} - a_{3} = 2\times11 - 8 = 22 - 8 = 14$ .

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