Find a formula for the general term of the sequence, assuming thatthe pattern of the rst few terms continues.(a){ 12 , 23 , 34 , 45 , 56 , . . .}(b){−1, 12 , − 16 , 124 , − 1120 , . . .}(c){1, 13 , 15 , 17 , 19 , . . .}(d) {5, 1, 5, 1, 5, 1, . . .}

To find the formula for the general term of each sequence, we need to analyze the pattern in the given terms.

(a) The pattern in the sequence {12, 23, 34, 45, 56, ...} is that each term is obtained by adding 11 to the previous term. So, the general term can be written as T(n) = 11n + 1, where n is the position of the term in the sequence.

(b) In the sequence {-1, 12, -16, 124, -1120, ...}, the pattern is not as straightforward. However, we can observe that each term alternates between positive and negative values and is obtained by multiplying the previous term by a certain factor. Looking closely, we can see that the factor alternates between 13 and -8. So, the general term can be written as T(n) = (-1)^(n+1) * 13^(n-1) * 8, where n is the position of the term in the sequence.

(c) The sequence {1, 13, 15, 17, 19, ...} follows a pattern where each term is obtained by adding 2 to the previous term. So, the general term can be written as T(n) = 2n - 1, where n is the position of the term in the sequence.

(d) The sequence {5, 1, 5, 1, 5, 1, ...} repeats the pattern of alternating between 5 and 1. So, the general term can be written as T(n) = 4 - 3^(n mod 2), where n is the position of the term in the sequence.