Final answer:
The nth term of the sequence 14, 1014, 2014, 3014, 4014 is found using the formula for arithmetic sequences, an = 14 + (n-1) × 1000, where n is the position of the term in the sequence.
Step-by-step explanation:
To determine the nᵗʰ term of the given sequence 14, 1014, 2014, 3014, 4014, we can see that each term increases by 1000 from the last. Therefore, the sequence represents an arithmetic progression where each term is 1000 more than the previous term except the first term which starts at 14. Starting from the first term (14), the nth term can be found by adding the common difference (1000) to the first term, multiplied by (n-1), because we do not need to increase the first term.
The general formula for the nth term of an arithmetic sequence is an = a1 + (n-1) × d, where a1 is the first term and d is the common difference. For this sequence, a1 = 14 and d = 1000. Applying the formula gives the nth term as an = 14 + (n-1) × 1000.
The given sequence is: 14, 1014, 2014, 3014, 4014. To determine the nᵗʰ term, we can observe that each term starts with the digit n and ends with 014. Therefore, the nᵗʰ term can be written as n014, where n represents the position of the term in the sequence.
For example, the first term is the 1ᵗʰ term, so it is 1,014. The second term is the 2ᵗʰ term, so it is 2,014. And so on.
Therefore, the formula to find the nᵗʰ term is n014.