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Algebra
Level
3
a three term arithmetic sequence of common difference of 5 will form a geometric sequence if the first term will decreased by 2,the second term will increased by 1 and the third term will increased by 12 .what is sum of the arithmetic sequence?
75
45
60
30
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1 solution
we represent the 1st term as x 2nd x+5 3rd x+10 then we have x-2,x+6,x+12 as a geometric sequence we have x+6/x-2=x+22/x+6 we simplify we have 8x=80 or x=10 substitute the value x=10 x+5=15 x+10=20 therefore the sum is 45