Beginning with n = 1, write the first four terms of the...

Beginning with n = 1, write the first four terms of the sequences whose nth terms, or general terms, are given by: a) an = 3+(-1)^{n+1} b) an = frac{(n+1)!}{2^n} A sequence defined recursively has the formula a1 = -2 and an = -3a_{n-1}+4 for n ? 2. Compute the first four terms of the sequence.

Transcript

00:01 So in this case we need to write first four term of the sequence whose nth or general term is given so in first part a n is given as 3 plus minus 1 to the power n plus 1 so writing for the first 4 term we need to put n equals to 1 so a 1 would be simply 3 plus minus 1 to the power 2 and that is nothing but 3 plus 1 equals to 4 a 2 would be simply 3 plus minus 1 to the power 3 and that is nothing but if we talk about a 3 so this would be 3 plus minus 1 to the power 4 and that is nothing but 4 now if we talk about 4 a 4 that is 3 plus minus 1 to the power 5 and that is 2 again so in this case we have 4 thermal 4 thermal term as 4 to 4 and 2 now moving to the next part a n is given as n plus 1 factorial upon 2 to the power n so in this case if we put n equals to 1 so a 1 would be simply 2 factorial upon 2 to the power 1 that is 2 upon 2 and that is now if we talk about a 2 a 2 would be simply 3 factorial upon 2 square 3 factorial is 1 into 2 2 that is 6 upon 2 square is 4 that is nothing but 3 upon 2 now k 3 would be simply 4 factorial upon 2 to the power 3 so this is nothing but 1 into 2 into 3 into 4 is 24 upon 2 cube is 8 and that is nothing but 3.

02:21 Now if we talk about a 4 that is simply 5 factorial upon 2 to the power 4 and that is 1 upon 120 upon 16 so we can simplify it further as in 8 table it will cut by 2 and it will cut by 15 so this would be 15 upon 2.

02:47 So first 4 term in this case would be 1 3 by 2 3 by 2 3 15 by 2 and so on now i'm discussing the last part sequence is defined as formula a 1 as minus 2 and a n equals to minus 3 a n minus 1 plus 4 and is later than or equal to 2 compute the first 4 term of this sequence so if we put n equals to 2 here so we will have a 2 is equal to minus 3 a 1 a1 is minus 2 plus 4 and that is 6 plus 4 and that is 10.

03:43 So from here a2 is 10...

Question

Beginning with n = 1, write the first four terms of the sequences whose nth terms, or general terms, are given by: a) an = 3+(-1)^{n+1} b) an = frac{(n+1)!}{2^n} A sequence defined recursively has the formula a1 = -2 and an = -3a_{n-1}+4 for n ? 2. Compute the first four terms of the sequence.

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