The sum of fourth and tenth term of an A.P is 12. Find the sum of the first 13 terms of the progression.
(a)78 (b)46 (c)52 (d)None

• For any Arithmetic Progression, the n'th term can be written as (a + (n-1)d),
  where 'a' = first term,
  'd' = Common difference between two terms,
  'n' = number of terms.
  e.g. 1st term = a + 0d = a
  2rd term = a+d,
  3rd term = a+2d,..and so on.
  
  The sum of the fourth and tenth term of an arithmetic progression is 12.
  4th Term + 10th Term = 12
  => (a+3d) + (a+9d) = 12
  => 2a + 12d = 12
  
  Now,,the sum of the first 13 terms of the arithmetic progression is,,,
  
  Sum of n terms of a arithmetic progression is given by ,,
  Sum=n(a+l)/2,
  where 'n' = number of terms, 'a' = first term, and 'l' = last term
  
  Sum of first 13 terms = 13(1st term+13th term)/2
  => 13(a+(a+12d))/2
  => 13(2a+12d)/2
  => (13)(12)/2
  => 78 is the Answer....
• 4 years agoHelpfull: Yes(4) No(0)