Calculate 81860

The two terms of the geometric sequence are a2=12 and a5=three halves.
a) calculate the tenth term of the sequence.
b) calculate the sum of the first 8 terms of the sequence.
v) how many first terms of the sequence need to be added so that the sum is equal to 45?

Correct answer:

a10 =  3/64
s8 =  47.8125
n =  4

Step-by-step explanation:

a2=12 a5=3/2=23=121=1.5  a5 = a2   q3  q=3a5/a2=31.5/12=21=0.5  a10=a5 q5=1.5 0.55=643=0.0469
a1=a2/q=12/0.5=24  s8=a1 q1q81=24 0.510.581=16765=471613=47.8125
s=45  s = a1   q1qn1  s/a1  (q1) = qn1  C=s/a1 (q1)+1=45/24 (0.51)+1=161=0.0625  qn=C  n ln q = ln C  n=ln(C)/lnq=ln0.0625/ln0.5=4

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