# Geometric progression

If for a g.p. S2=8 and s4=80,find its first term and the common ratio.

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1. s2 = s1 * q

s4 = s1 * q ^ 3

8 = s1 * q

40 = s1 * q ^ 3

s1 * q ^ 3 = s1 * q * q ^ 2

40 = s1 * q ^ 3 = ( s1 * q ) * q ^ 2 = 8 * q ^ 2

40 = 8 * q ^ 2

40 / 8 = q ^ 2

5 = q ^ 2

q = ± sqrt ( 5 )

You can construct two g.p.

1.

8 = s1 * g

8 = s1 / sqrt ( 5 )

s1 = 8 / sqrt ( 5 )

2.

8 = s1 * g

8 = s1 / - sqrt ( 5 )

s1 = - 8 / sqrt ( 5 )

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