Question

nth term of a geometric sequence learn it now score: 5/9 possible: 100 you only have 4 questions left to raise your score. question find the 18th term of the geometric sequence 10, -60, 360, ... answer

Explanation:

Step1: Identify common ratio \( r \)

The geometric sequence is \( 10, -60, 360, \dots \). The common ratio \( r \) is found by dividing the second term by the first term: \( r=\frac{-60}{10}=-6 \).

Step2: Recall geometric sequence formula

The formula for the \( n \)-th term of a geometric sequence is \( a_n = a_1 \cdot r^{n - 1} \), where \( a_1 \) is the first term, \( r \) is the common ratio, and \( n \) is the term number. Here, \( a_1 = 10 \), \( r = -6 \), and \( n = 15 \).

Step3: Substitute values into formula

Substitute \( a_1 = 10 \), \( r = -6 \), and \( n = 15 \) into the formula: \( a_{15}=10\times(-6)^{15 - 1} \).
Simplify the exponent: \( 15 - 1 = 14 \), so \( a_{15}=10\times(-6)^{14} \).
Calculate \( (-6)^{14} \): since the exponent is even, \( (-6)^{14}=6^{14} \). \( 6^{14}=78364164096 \).
Then multiply by 10: \( a_{15}=10\times78364164096 = 783641640960 \).

Answer:

\( 783641640960 \)