Question

the sum of three consecutive terms in a geometric progression is 42 and their product is 512 what is the largest number​

Answer 1

Answer:

Three terms are 2,  8  and 32.

Step-by-step explanation:

The sum of three consecutive terms of a geometric progression is =42

a + ar + ar^2 = 42

a(1 + r + r^2) = 42

Their product = 512

a . ( ar ) . ( ar )^2 = 512

a^3 . r^3 = 512

( ar )^3 = 8^3

ar = 8  

a.( 1 + r + r^2 ) / ar = 42 / 8 = 21 / 4

( 1 + r + r^2 ) / r = 21 / 4

4.( 1 + r + r^2 ) / r = 21 r

4 + 4r + 4r^2 = 21.r

4 + 4r + 4r^2 - 21.r  = 0

4r^2 - 17r + 4 = 0

4r^2 - 16r - r + 4 = 0

4r( r - 4 ) - 1 (r - 4 ) = 0

(4r - 1) . (r - 4) = 0

(4r - 1) =0    or  (r - 4) = 0

4r = 1   or  (r = 4)

r = 1/4    or   r = 4

if r = 4,

in ar= 8

a.4= 8

a = 8 / 4 = 2

then

3 terms are a=2,

                    ar=8, and

                   ar^2 = 2(4)^2 = 2x 16 = 32

check:

sum = 2+8+32 = 42 ⩗

product = 2 x 8 x 32 = 512 ⩗