What will be the 9th term in the sequence (3, −6, 12, −24, …)?
Answer and explanation
Correct answer: 768
The governing concept is a geometric sequence, in which each term is obtained by multiplying the previous term by a constant common ratio. Here the ratio is −6 ÷ 3 = −2, and the later terms confirm it: 12 ÷ (−6) = −2 and −24 ÷ 12 = −2. Thus the explicit rule is a_n = 3(−2)^(n−1). For n = 9, a_9 = 3(−2)^8 = 3 × 256 = 768. The exponent is even, so the power is positive; therefore option C is correct. The negative choices ignore the even power, while 384 is half the required value.
Frequently asked questions
What is the correct answer to this question?
768
Why is this the correct answer?
The governing concept is a geometric sequence, in which each term is obtained by multiplying the previous term by a constant common ratio. Here the ratio is −6 ÷ 3 = −2, and the later terms confirm it: 12 ÷ (−6) = −2 and −24 ÷ 12 = −2. Thus the explicit rule is a_n = 3(−2)^(n−1). For n = 9, a_9 = 3(−2)^8 = 3 × 256 = 768. The exponent is even, so the power is positive; therefore option C is correct. The negative choices ignore the even power, while 384 is half the required value.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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