How many terms are in the following sequence that follows? 3,7,11,....,439
looks like an arithmetic sequence with
a = 3
d = 4
term(n) = 439
a + (n-1)d = 439
3 + (n-1)(4) = 439
4n - 4 = 436
4n = 440
n = 110
there are 110 terms
arithmetic sequence
Xn - a + d(n-1)
here a = first term = 3
d = constant difference = 4
Xn = 439
so
439 = 3 + 4(n-1)
439 = 3 * 4 n - 4
440 = 4 n
n = 110
To find the number of terms in a sequence, you need to determine the pattern or progression in the given sequence. In this case, we can observe that each term in the sequence is obtained by adding 4 to the previous term.
Starting with the first term, which is 3, we can find subsequent terms by adding 4 repeatedly:
3 + 4 = 7
7 + 4 = 11
11 + 4 = 15
...
We continue this process until we reach the final term in the sequence. We can see that the sequence grows by adding 4 each time until it reaches 439.
To determine the number of terms, we need to count how many times we added 4 to reach 439. We can set up an equation and solve it:
3 + 4n = 439 (where n represents the number of times 4 is added)
Subtracting 3 from both sides:
4n = 436
Dividing both sides by 4:
n = 109
Therefore, the number of terms in the given sequence is 109.