# Geometric sequence 4

It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).

Result

s23 =  83.26

#### Solution:

$a_{ 3 } = a_1 q^{ 3-1} = 7 \ \\ a_{ 12 } = a_1 q^{ 12-1} = 3 \ \\ \ \\ 3/7 = q^ { 12 - 3 } = q^{ 9} \ \\ q = \sqrt[ 9 ]{ 3/7 } = 0.9102 \ \\ \ \\ a_1 0.9102^{ 3-1} = 7 \ \\ a_1 = 7 / 0.9102^{ 3-1} = 8.4503 \ \\ \ \\ s_{ 23 } = a_1 \dfrac{q^{ 23 } -1 }{q-1} = 8.4503 \dfrac{ 0.9102^{ 23 } -1 }{ 0.9102-1} = 83.26$

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