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 If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is       
  • a)
    13
  • b)
    9       
  • c)
    21
  • d)
    17
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the sum of three consecutive terms of an increasing A.P. is 51 and ...
  • Let 3 consecutive terms A.P is a –d, a , a + d. and the sum is 51
  • so, (a –d) + a + (a + d) = 51
  • ⇒ 3a –d + d = 51
  • ⇒ 3a = 51
  • ⇒ a = 17
  • The product of first and third terms is 273
  • So  it stand for ( a –d) (a + d) = 273
  • ⇒ a2 –d2 = 273
  • ⇒ 172 –d 2 = 273
  • ⇒ 289 –d 2 = 273
  • ⇒  d 2 = 289 –273
  • ⇒ d 2 = 16
  • ⇒ d = 4
  • Hence the 3rd terms ( a+d )= 17 + 4 =  21
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