Question

The sum of q terms of an A.P IS 162.The ratio of the sixth term and the 13th term is 1:2. Find the first and the 15th term of this A.P.

Answer 1

Heya User,

--> [ a + 5d ] : [ a + 12d ] = 1 : 2
=> 2 [ a + 5d ] = [ a + 12d ]
=> a = 2d √√√

Sum = [ a + ( a + d ) + ..... + { a + ( n - 1 )d } ] 
         = [ a + 3a + 5a + ... + { a + ( n - 1 )2a } ]
         = a [ 1 + 3 + ... + ( 2n - 1 ) ]
         = n²a

Now, sum of 'q' terms = 162
=> q²a = 162
=> q²a = 9²(2)  || 1²(162) || 3²( 18 )
=> a = 2 || 162 || 18 √√
=> d = 4 || 324 || 36

=> 15th term = a + 14d = a + 28a = 29a = 58 || 4698 || 522


In case that's '9' and not 'q' , 'a' = 2 ; d =  4 ; 15th term = 58 √√