Geometric sequence

In the geometric sequence, is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.

Correct answer:

q =  -1.5157
a1 =  -5.7435

Step-by-step explanation:

a4​=20 a9​=−160  a9​ = q5⋅ a4​  q = 5a9​/a4​​ q<0 +−+−+− q=−5160/20​=−1.5157
a4=q3⋅ a1  a1=a4/q3=20/(−1.5157)3≐−5.7435   Verifying Solution:   A4=a1⋅ q3=(−5.7435)⋅ (−1.5157)3=20 A9=a1⋅ q8=(−5.7435)⋅ (−1.5157)8=−160a_{4} = q^3 \cdot \ a_{1} \ \\ \ \\ a_{1} = a_{4}/q^3 = 20/(-1.5157)^3 \doteq -5.7435 \ \\ \ \\ \text{ Verifying Solution: } \ \\ \ \\ A_{4} = a_{1} \cdot \ q^3 = (-5.7435) \cdot \ (-1.5157)^3 = 20 \ \\ A_{9} = a_{1} \cdot \ q^8 = (-5.7435) \cdot \ (-1.5157)^8 = -160

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