Find three terms of gp whose sum is 63 and product is 1728
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Answer: The gp is 3,12,48
Step-by-step explanation:
Let the three terms be a/r,a,ar
Where the first term is "a" and the common difference is "r"
Therefore,
Product=> a/r *a*ar=1728
=>a=12
Sum =63 (given)
a/r +a+ar=63...... (i)
we know,
a=12
Now,
Putting the value of a in (i)
12/r +12+12r=63
=> (12 +12r+12r^2)/r=63r
=> 12 +12r+12r^2=63r
=>12r^2 -51r+12=0
=> 12r^2-48r-3r+12=0
=> 12r (r-4)-3 (r-4)=0
=> (12r-3)(r-4)=0
We can say.
12r-3=0 or r-4=0
r=4 (in both cases)
So the gp is a/r,a,ar
12/4,12,12*4
3,12,48 (Answer)
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