In a geometric sequence, each term is found by multiplying the previous term by a constant factor known as the common ratio (r). In this case, you have:
- First term (a1): 30
- Common ratio (r): 12
The formula for the n-th term of a geometric sequence can be represented as:
an = a1 × r(n-1)
To find the fourth term (a4), substitute n=4 into the formula:
a4 = a1 × r(4-1)
Substituting the known values:
a4 = 30 × 123
Now, calculate 123:
12 × 12 × 12 = 1728
Now, substitute this back into the equation for a4:
a4 = 30 × 1728
Finally, calculate:
30 × 1728 = 51840
Thus, the value of the fourth term in the geometric sequence is:
a4 = 51840
In conclusion, for the given geometric sequence where the first term is 30 and the common ratio is 12, the fourth term is 51840.