The arithmetic sequence 2, 6, 10, … 90. The number of terms in the sequence is .....
a = 2, d = 4
term(n) = a + (n-1)d
2 + (n-1)(4) = 90
4(n-1) = 88 , divide each side by 4
n-1 = 22
n = 23
you have 23 terms
To find the number of terms in an arithmetic sequence, you need to determine the common difference and use it to find the nth term of the sequence. Then, you can divide the last term of the sequence by the nth term to find the number of terms.
In this case, we have an arithmetic sequence 2, 6, 10, ... with a common difference of 4. To find the nth term, we can use the formula:
nth term = first term + (n - 1) * common difference
In this sequence, the first term is 2 and the common difference is 4. So, the nth term can be written as:
nth term = 2 + (n - 1) * 4
We know that the last term in the sequence is 90. So, we can substitute this value into the formula and solve for n:
90 = 2 + (n - 1) * 4
Simplifying the equation:
90 = 2 + 4n - 4
90 = 4n - 2
Adding 2 to both sides:
92 = 4n
Dividing both sides by 4:
n = 92/4
n = 23
Therefore, the number of terms in the sequence is 23.