Answer :
Main Answer:
A. The 8th term of the geometric sequence is 2187.
Therefore, the correct answer is b) -2187.
Explanation:
To find the 8th term of the geometric sequence, we first identify the common ratio (r) by dividing the second term by the first term: [tex]\( r = \frac{{-21}}{{7}} = -3 \).[/tex] Then, we use the formula for the nth term of a geometric sequence: [tex]\( a_n = a_1 \times r^{(n-1)} \).[/tex] Substituting the values [tex]\( a_1 = 7 \) and \( r = -3 \)[/tex] into the formula, we get [tex]\( a_8 = 7 \times (-3)^{(8-1)} = 7 \times (-3)^7 = 7 \times (-2187) = -15309 \).[/tex] Therefore, the 8th term of the sequence is [tex]\( -15309 \),[/tex] which corresponds to option D.
Therefore, the correct answer is b) -2187.
