Find the number of term s in the following arithmetic sequence.
3, 9, 15, 21... 123
a = 3 , d = 6
term(n) = a + (n-1)d
123 = 3 + (n-1)(6)
120 = 6n - 6
126 = 6n
n = 126/6 = 21
there are 21 terms
To find the number of terms in an arithmetic sequence, you need to determine the common difference between consecutive terms. The common difference is the amount by which each term increases or decreases.
In this arithmetic sequence, the first term is 3, and each subsequent term increases by 6 (9 - 3 = 6, 15 - 9 = 6, 21 - 15 = 6, and so on). Therefore, the common difference in this sequence is 6.
To find the number of terms, you can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.
In this case, we have:
123 = 3 + (n - 1)6
Simplifying the equation:
123 = 3 + 6n - 6
123 = 6n - 3
Adding 3 to both sides:
126 = 6n
Dividing both sides by 6:
n = 21
Therefore, the number of terms in the given arithmetic sequence is 21.