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iv)
The sum of
four numbers in G.P. is 80 and the A.M. between the
first and the last is 28. Show that the numbers are 2, 6, 18, 54.
​

Sagot :

Sreedevi102idn

Answer:

Step-by-step explanation:

Given numbers : 2 , 6, 18, 54

Since common ration between numbers,

[tex]common \ ratio \ in \ GP , \ r = \frac{a_n}{a_{n-1}} = \frac{6}{2} = 3[/tex]

So the numbers are in GP.

Now Sum of the numbers = 2 + 6 + 18 + 54 = 80

AM, arithmetic mean between first and last number :

                                                                             [tex]\frac{54+2}{2} = \frac{56}{2} =28[/tex]

All the conditions are true.

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