ferminpequeno9 ferminpequeno9
  • 13-06-2017
  • Mathematics
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Find the sum of the first five terms of the geometric series in which a2 is -12 and a5 is 768

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ghanami
ghanami ghanami
  • 13-06-2017
hello : 
the general term is : an = ap×q^(n-p)...... q : common ratio 
n=5 and p=2  : a5 = a2×q^(5-2)
                        768 = -12q^3
q^3 = 768/(-12)
q^3 = - 64
but : 64 = 4^3
q^3 =(-4)^3....   -4^3 =(- 4)^3
q= - 4 
calculate the first term : a1
a2 = a1 q
a1 =a2/q 
a1 = -12/-4
a1 = 3
the sum of the first five terms  is : S= a1 × (1- q^n)/(1- q)
a1 = 3        q =-4       n =5 
S = 3(1-(-4)^5)/(1-(-4)).....calculate
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