Three numbers a,b,12 are in gp and a,b,9 are in ap then a and b are
Answers
Answer:
Step-by-step explanation:
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Answer:
The value of values of a and b are 3 and 6 or 27 and 18.
Step-by-step explanation:
Geometric progression is used for a, b, and 12.
∴a₁=a , a₁r=b
Where a₁ = the first term and r = the common ratio
=> r=b/a
12 /b =r
⇒ 12 /b= b/a
⇒b^2 =12a————————-i
Additionally, the numbers 9, a, and b from an AP.
b−a=9−b
⇒2b=9+a
⇒a=2b−9---------------------------------ii
From Equations i and ii, we obtain
⇒b ^2 = 12(2b - 9)
⇒b^ 2 = 24b - 108
⇒b ^2 - 24b+108= 0.
⇒b ^2 −18b−6b+108=0
⇒b(b−18)−6(b−18)=0
⇒b=6 or b=18.
If b=6, then
a=b^2/12
=>a=(6 x 6)/12
=>a=3
When b = 18,
⇒a = b^2./12
⇒a=(18 x 18) /12
⇒a=27
Hence, the required values of a and b are 3 and 6 or 27 and 18.
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