IIT JEE , AIEEE Forum - Mathematics , Algebra

shinu.sharma

In a set of 4 numbers , 1st 3 are in GP , last 3 are in AP , with common difference = 6

if first no. = 4th no.

then find the 4 numbers

plzzzzzz helppp

iitkgp_bipin

The three numbers of an AP with common difference 6 can be written as a-6, a, a+6.

These are the last three numbers.

Now 1st no. = 4th no.= a+6

So 4 numbers are a+6, a-6, a, a+6

1st three of them are in GP i.e. a+6, a-6, a are in GP.

Hence common ratio of GP = (a-6)/(a+6) = a/(a-6)

(a-6)² = a(a+6)

a² - 12a + 36 = a² + 6a

18a = 36

a = 2

Hence the numbers are 8, -4, 2, 8.

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