The given sequence is 3, 6, 9, 12,...
To find the general term (an) of this sequence, we can observe that each term is obtained by adding 3 to the previous term.
We can express this pattern as:
a1 = 3 (since n = 1 for the first term)
a2 = a1 + 3 = 3 + 3 = 6
a3 = a2 + 3 = 6 + 3 = 9
a4 = a3 + 3 = 9 + 3 = 12
...
So, the general term (an) of this sequence is obtained by adding 3 to the previous term:
an = an-1 + 3
Using this formula, we can calculate any term in the sequence. For example, if we want to find the value of the 10th term (a10), we can use the formula:
a10 = a9 + 3
= (a8 + 3) + 3
= ((a7 + 3) + 3) + 3
= (((a6 + 3) + 3) + 3) + 3
= (((((a5 + 3) + 3) + 3) + 3) + 3) + 3
= ((((((a4 + 3) + 3) + 3) + 3) + 3) + 3) + 3
= ((((((12 + 3) + 3) + 3) + 3) + 3) + 3) + 3
= ((((((15 + 3) + 3) + 3) + 3) + 3) + 3) + 3
= ((((((18 + 3) + 3) + 3) + 3) + 3) + 3) + 3
= ((((((21 + 3) + 3) + 3) + 3) + 3) + 3) + 3
= ((((((24 + 3) + 3) + 3) + 3) + 3) + 3) + 3
= ((((((27 + 3) + 3) + 3) + 3) + 3) + 3) + 3
= ((((((30) + 3) + 3) + 3) + 3) + 3) + 3
= (((((33) + 3) + 3) + 3) + 3) + 3
= ((((36) + 3) + 3) + 3) + 3
= (((39) + 3) + 3) + 3
= ((42) + 3) + 3
= 45
So, the 10th term (a10) of the sequence is 45.
In general, the nth term (an) of the sequence can be found by using the formula:
an = a1 + (n-1) * 3
This formula allows us to calculate any term in the sequence based on its position (n).