2.7n +3.5n -5 is divisible by 24 ?
 

Asked by PALLAVI GARG | 29th Jul, 2014, 01:50: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n space 2 cross times 7 n plus 3 cross times 5 n minus 5 A s s u m e space t h a t space space n equals 1 2 cross times 7 n plus 3 cross times 5 n minus 5 equals 2 cross times 7 cross times 1 plus 3 cross times 5 cross times 1 minus 5 equals 14 plus 15 minus 5 equals 24 T h u s comma space t h e space g i v e n space e x p r e s s i o n space i s space t r u e space f o r space n equals 1 N o w space l e t space u s space a s s u m e space t h a t space t h e space g i v e n space e x p r e s s i o n space i s space d i v i s i b l e space b y space 24 space f o r space n equals k W e space n e e d space t o space p r o v e space t h a t space t h e space g i v e n space e x p r e s s i o n space i s space d i v i s i b l e space b y space 24 space f o r space n equals k plus 1 C o n s i d e r space t h e space g i v e n space e x p r e s s i o n space f o r space n equals k plus 1 2 cross times 7 open parentheses k plus 1 close parentheses plus 3 cross times 5 open parentheses k plus 1 close parentheses minus 5 equals 14 k plus 14 plus 15 k plus 15 minus 5 equals 29 k plus 24 I t space i s space c l e a r space f r o m space t h e space a b o v e space e x p r e s s i o n space t h a t space i t space i s space n o t space d i v i s i b l e space b y space 24.

Answered by Dharma Teja | 30th Jul, 2014, 10:11: AM