Question

The product of the first 11 terms in a geometric progression is 2048. Find the 6th term?

Answer 1

The product of the first 11 terms in a geometric progression is 2048. Find the 6th term?

let first 11 terms in geometric progression are ; a/r^5, a/r^4, a/r^3, a/r^2, a/r, a , ar, ar^2, a^3, ar^4, ar^5.

a/c to question,

product of 11 terms = 2048

or, (a/r^5 × a/r^4 × a/r^3 × a/r^2 × a/r × a × ar × ar^2 × ar^3 × ar^4 × ar^5) = 2048

or, a¹¹ = 2048 = (2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 )

or, a¹¹ = 2¹¹

or, a = 2

now see series here 6th term is a.

so, 6th term , a = 2.

Answer 2

Answer:

2

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