Sequences & SerieseasyFree

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

3

, then the product of the first seven terms is

3^4

3^7

correct

7^4

4^7

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

r

and write the seven terms as

\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

r

cancel out completely, so the product is simply

a^7

. Step 3: The middle (fourth) term here is

a

, and we are told it equals

3

. Hence the product is

a^7=3^7.

Correct answer: (2)

Still stuck on this question?Ask your doubt on WhatsApp

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.