1. Find three numbers in AP whose sum is 15 and the product is 80.
  2. If the sum of first n terms of an AP is 4n*-n, find the 12th term.
  3. The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, find the AP.

Asked by godson babuji | 5th Nov, 2014, 02:13: AM

Expert Answer:

 
left parenthesis 1 right parenthesis L e t space f i r s t space n u m b e r space b e space x space a n d space c o m m o n space d i f f e r e n c e space i s space d. S o space t h e space f i r s t space t h r e e space n u m b e r s space i n space a p space b e space x comma space x plus d comma space x plus 2 d.  S u m space o f space t h e space f i r s t space t h r e e space n u m b e r s space i n space a p space i s space 15. rightwards double arrow space x plus left parenthesis x plus d right parenthesis plus left parenthesis x plus 2 d right parenthesis space equals space 15 space rightwards double arrow space 3 x plus 3 d space equals space 15 space rightwards double arrow space x plus d space equals space 5 rightwards double arrow space x space equals space 5 minus d space...... left parenthesis i right parenthesis  P r o d u c t space o f space t h e space f i r s t space t h r e e space n u m b e r s space i n space a p space i s space 80. rightwards double arrow space x left parenthesis x plus d right parenthesis left parenthesis x plus 2 d right parenthesis space equals space 80 space rightwards double arrow space left parenthesis 5 minus d right parenthesis space left parenthesis 5 minus d plus d right parenthesis left parenthesis space 5 minus d plus 2 d right parenthesis equals 80 space space space space space space space space left square bracket f r o m space left parenthesis i right parenthesis right square bracket rightwards double arrow 25 minus d squared equals 16 rightwards double arrow d equals plus-or-minus 3   w h e n space d equals 3 rightwards double arrow space x space equals space 5 minus 3 equals 2  w h e n space d equals minus 3 rightwards double arrow space x space equals space 5 plus 3 equals 8  S o space t h e space f i r s t space t h r e e space n u m b e r s space i n space a p space a r e space 2 comma 5 comma 8 space o r space space 8 comma 5 comma 2
Please post one question per query.

Answered by Vijaykumar Wani | 5th Nov, 2014, 10:47: AM