An algebra problem by A Former Brilliant Member

Algebra Level 2

− 13 10 , a , b , − 63869 7290 -\dfrac{13}{10}, a, b, -\dfrac{63869}{7290} follows a geometric progression. Find the average of a a and b b .

-2873/90 -2873/405 -2873/810 -2873/800

A Former Brilliant Member by A Former Brilliant Member

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1 solution

An = A1 * r^(n-1)

− 63869 7290 \frac{-63869}{7290} = − 13 10 \frac{-13}{10} * r 3 r^3

4913 729 \frac{4913}{729} = r 3 r^3

17 9 \frac{17}{9} = r r

There are 2 geometric means, so the number of terms is four.

A1 = − 13 10 \frac{-13}{10}

A2 = − 13 10 \frac{-13}{10} * 17 9 \frac{17}{9} = − 221 90 \frac{-221}{90}

A3 = − 221 90 \frac{-221}{90} * 17 9 \frac{17}{9} = − 3757 810 \frac{-3757}{810}

A4 = − 63869 7290 \frac{-63869}{7290}

The average of the two arithmetic means is,

(A2 + A3) /2 = − 2873 810 \frac{-2873}{810}

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