If a_(1)=1,a_(2)=3 and a_(n)=2a_(n-1)-2a_(n-2) then find the value of a_(6). Answer:

Given Sequence and Formula: We are given the first two terms of the sequence: a_(1) = 1 and a_(2) = 3. We are also given the recursive formula for the sequence: a_(n) = 2a_(n-1) - 2a_(n-2). To find a_(6), we need to find the terms a_(3), a_(4), and a_(5) using the recursive formula.Find a_(3): Let's find a_(3) using the recursive formula: a_(3) = 2a_(2) - 2a_(1) = 2*3 - 2*1 = 6 - 2 = 4.Find a_(4): Now let's find a_(4) using the recursive formula: a_(4) = 2a_(3) - 2a_(2) = 2*4 - 2*3 = 8 - 6 = 2.Find a_(5): Next, we find a_(5) using the recursive formula: a_(5) = 2a_(4) - 2a_(3) = 2*2 - 2*4 = 4 - 8 = -4.Find a_(6): Finally, we find a_(6) using the recursive formula: a_(6) = 2a_(5) - 2a_(4) = 2*(-4) - 2*2 = -8 - 4 = -12.

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Q. If

a_{1}=1, a_{2}=3

and

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

then find the value of

a_{6}

\newline

Answer:

Given Sequence and Formula: We are given the first two terms of the sequence: $a_1 = 1$ and $a_2 = 3$ . We are also given the recursive formula for the sequence: $a_n = 2a_{n-1} - 2a_{n-2}$ . To find $a_6$ , we need to find the terms $a_3$ , $a_4$ , and $a_5$ using the recursive formula.
Find $a_{3}$ : Let's find $a_{3}$ using the recursive formula: $\newline$ $a_{3} = 2a_{2} - 2a_{1} = 2\times3 - 2\times1 = 6 - 2 = 4$ .
Find $a_{4}$ : Now let's find $a_{4}$ using the recursive formula: $\newline$ $a_{4} = 2a_{3} - 2a_{2} = 2\times 4 - 2\times 3 = 8 - 6 = 2$ .
Find $a_{5}$ : Next, we find $a_{5}$ using the recursive formula: $\newline$ $a_{5} = 2a_{4} - 2a_{3} = 2\times2 - 2\times4 = 4 - 8 = -4$ .
Find $a_{6}$ : Finally, we find $a_{6}$ using the recursive formula: $\newline$ $a_{6} = 2a_{5} - 2a_{4} = 2*(-4) - 2*2 = -8 - 4 = -12$ .