Final answer:
The 15th term of the geometric sequence 7, -21, 63 is found using the formula for the nth term of a geometric sequence. With a common ratio of -3, the 15th term is calculated to be 33,480,783.
Step-by-step explanation:
The question asks for the 15th term of the geometric sequence 7, -21, 63. To find the 15th term, we must first identify the common ratio (r). This can be found by dividing the second term by the first term: r = -21 / 7 = -3.
With the common ratio and the first term (a1 = 7), we can use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1).
Substituting the given values for the 15th term gives us a15 = 7 × (-3)(15-1). Solving this, we get:
a15 = 7 × (-3)14
= 7 × 4,782,969
= 33,480,783.
Hence, the 15th term of the sequence is 33,480,783.