Question

in a sequence of numbers, a₃=3, a₄=7, a₅=11, a₆=15, and a₇=19. based on this information, which equation can be used to find the nth term in the sequence, an?​

Answer 1

The nth term of the sequence with given terms a_3=3, a_4=7, a_5=11, a_6=15, and a_7=19 is calculated using the arithmetic sequence formula a_n = a_1 + (n - 1) * d, resulting in a_n = -5 + (n - 1) * 4.

Step-by-step explanation:

Given the terms of the sequence a_3=3, a_4=7, a_5=11, a_6=15, and a_7=19, we need to find the nth term of the sequence. Observing the pattern, we can see that each term is increasing by 4. Thus, the sequence is an arithmetic sequence with a common difference of 4. To find the nth term, we can use the general formula for an arithmetic sequence, which is a_n = a_1 + (n - 1) * d, where a_1 is the first term and d is the common difference. Since a_3 is 3, we can deduce that a_1 would be 3 - 2*4 = -5. Therefore, the equation to find the nth term is a_n = -5 + (n - 1) * 4.