Q5 / 118 · NTA Abhyas (JEE Main) 2020 · Mathematics · Sequences and Series

If 2, 7, 9 and 5 are subtracted respectively from four numbers in geometric progression, then the resulting numbers are in arithmetic progression. The smallest of the four numbers is

  • Correct answer
    A
    –24
  • B
    –12
  • C
    6
  • D
    3

Solution

Let the numbers be a,ar,ar2,ar3 ,
⇒a-2,ar-7,ar2-9 and ar3-5 are in A.P.
⇒a-2+ar2-9=2ar-7 and ar-7+ar3-5=2ar2-9
⇒a+ar2=2ar-3 and ar+ar3=2ar2-6
⇒1+r2=2r-3a and 1+r2=2r-6ar
⇒3a=6ar⇒r=2
⇒3a=2r-1-r2=4-1-4=-1⇒a=-3
So, the numbers are –3,–6,–12,–24

Hence, the correct answer is option: 'A'.

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