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Product of First Seven Terms of a GP, 4th Term 3 | JEE

JEE Maths question with a full step-by-step solution.

Question
If the fourth term of a G.P. is 33, then the product of the first seven terms is
A343^4
B373^7correct
C747^4
D474^7
Solution
Step 1: Since the number of terms is odd (seven), it is convenient to take them symmetrically about the middle term. Let the common ratio be rr and write the seven terms as
ar3, ar2, ar, a, ar, ar2, ar3.\frac{a}{r^3},\ \frac{a}{r^2},\ \frac{a}{r},\ a,\ ar,\ ar^2,\ ar^3.
 Step 2: Multiplying them together, the powers of rr cancel out completely, so the product is simply a7a^7. Step 3: The middle (fourth) term here is aa, and we are told it equals 33. Hence the product is
a7=37.a^7=3^7.
 Correct answer: (2)
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