Answer:
(a) To find an expression for the nth term of the arithmetic sequence, we first need to determine the common difference. We can see that each term increases by 4, so the common difference is 4. To find the nth term, we'll use the formula for the nth term of an arithmetic sequence: a₁ = a + (n-1)d. where is the first term and d is the common difference. Thus, the nth term of the sequence is:
a₁ = -3+ (n-1)-4
Simplifying this expression, we get:
a = 411-7
Therefore, the expression for the nth term of the given arithmetic sequence is 4-7, (b) We can check if 101 is a term in the second arithmetic sequenceis 4-7. (b) We can check if 101 is a term in the second arithmetic sequence by seeing if there is a value of n for which a₁ = 101
211-3=101
Adding 3 to both sides, we get:
211 = 104
Dividing by 2, we get:
11 = 52
Therefore, the term with value 101 appears as the 52nd term in the second arithmetic sequence.