Question

question 3735
17 what is the 10th term in the geometric sequence?
3, -9, 27, -81, ...
a 177,147
b 59,049
c -59,049
d -177,147

Explanation:

Step1: Identify first term and ratio

First term $a_1 = 3$, ratio $r = \frac{-9}{3} = -3$

Step2: Apply geometric sequence formula

Formula: $a_n = a_1 \cdot r^{n-1}$
For $n=10$: $a_{10} = 3 \cdot (-3)^{9}$

Step3: Calculate the value

$(-3)^9 = -19683$, so $3 \cdot (-19683) = -59049$? Wait no, wait $(-3)^9$ is $(-3)^{8+1}=(-3)^8*(-3)=6561*(-3)=-19683$, $3*(-19683)=-59049$? Wait wait the options have C as -59049, but wait let's check again: the sequence is 3, -9, 27, -81... so term 1:3, term2:-9, term3:27, term4:-81, term5:243, term6:-729, term7:2187, term8:-6561, term9:19683, term10:-59049. Oh right! So the answer is C. -59049.

Wait correction:

Step1: Find first term and ratio

$a_1=3$, $r=-3$

Step2: Use geometric term formula

$a_n=a_1r^{n-1}$

Step3: Compute 10th term

$a_{10}=3*(-3)^{9}=3*(-19683)=-59049$

Answer:

A. 177147