Question

Find the product of 11 terms in G.P whose 6th term is 5

Answer 1

@ganeshie8

Answer 2

Middle term is 5 this means

Answer 3

wow ! yes we can use symmetry

Answer 4

yesss

Answer 5

\[\large a_1 a_2 a_3 a_4 \cdots a_{11}\]

Answer 6

A_1 * A_11 = A _2 * A _10 Like this right

Answer 7

that looks perfect !!

Answer 8

5^11

Answer 9

!!!

Answer 10

middle term = geometric mean

Answer 11

\(\large a_6 = \sqrt{a_1 \times a_{11}} = \sqrt{a_2 \times a_{10}} = \cdots \)

Answer 12

5^11 is correct !

Answer 13

There is a formula for the product of n terms in G.P i saw it on wikipedia

Answer 14

http://en.wikipedia.org/wiki/Geometric_progression#Related_formulas

Answer 15

But we can't really use it here

Answer 16

\(\large a_1, a_1r, a_1r^2, \cdots \)

product = \(\large a_1 \times a_1r \times a_1r^2 \cdots \)

Answer 17

if there are n terms :

product = \(\large a_1^n r^{0 + 1 + 2 + \cdots n-1}\)

Answer 18

product = \(\large a_1^n r^{\frac{n(n-1)}{2}}\)

Answer 19

yes!

Answer 20

nice :)

Answer 21

Actually there is so much work done in this chapter especially by Euclid
I felt that doing some more 15 pages i would attain a mastery at this concept , but i was stumped by reading wikipedia

Answer 22

One can study a math concept till his death and still he won't learn everything

Answer 23

true ! cuz its so much fun that one doesn't feel like giving it up - so one pursues it till one's death xD

Answer 24

hahahhah