Question

The sum of the numbers in G.P. is $\frac{39}{10}$
and their product is 1. Let ‘m’ &
‘n’ be two possible first term. Then ‘m + n’ is

Answer 1

Let first three terms a/r, a, ar

A/C to question,

sum of first three terms = 39/10

= a/r + a + ar = 39/10

= a[ 1/r + 1 + r ] = 39/10------------(1)

again product of first three terms = 1

= a/r * a * ar = 1

= a^3 = 1 = 1^3

= a = 1, putting in equation (1)

we get, 1 [ 1/r + 1 + r ] = 39/10

= [ 1 + r + r^2 ] / r = 39/10

= 10 + 10r + 10r^2 = 39r

= 10r^2 - 29r + 10 = 0

= 10r^2 - 25r - 4r + 10 = 0

= 5r ( 2r - 5 ) - 2 ( 2r - 5) = 0

= ( 5r -2 ) ( 2r - 5 ) = 0

= r = 2/5 , 5/2

Now, for a = 1 and r = 2/5 three terms are ; 5/2 , 1 , 2/5

Now, a = 1 and r = 5/2 three terms are ; 2/5 , 1 , 5/2

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