Quantities 60183

Determine the remaining quantities in the finite geometric sequence, given: n = 4, an = 12.5, sn = 187.5, a1 = ?, q =?

Correct answer:

a1 =  100
q =  0.5

Step-by-step explanation:

n=4 a4​=12.5 s4​=187.5  a4​ = a1​⋅ qn−1 = a1​⋅ q3 s4​ = a1​⋅  q−1qn−1​ = a1​⋅  q−1q4−1​  s4​ =  q3a4​​ ⋅  q−1q4−1​ s4​ =  q3a4​​ ⋅  q−1(q2−1)(q2+1)​ s4​ =  q3a4​​ ⋅  q−1(q−1)(q+1)(q2+1)​ s4​ =  q3a4​​ ⋅ (q+1)(q2+1)  s4​/a4​ = q3(q+1)(q2+1) ​ s4​⋅ q3 = a4​⋅  (q+1)(q2+1)  q​=1 q=1/2=21​=0.5  a1​=q3a4​​=0.5312.5​=100
 Verifying Solution:  a2​=q⋅ a1​=21​⋅ 100=21⋅ 100​=2100​=50 a3​=q⋅ a2​=21​⋅ 50=21⋅ 50​=250​=25  s=a1​+a2​+a3​+a4​=100+50+25+12.5=2375​=18721​=187.5  q=21​=0.5

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