Question

Using Euclid's division algorithm, find whether the pair of numbers 847, 2160 are coprimes or not.

Answer 1

hello friend,
2160 = 2 * 847 + 466
847 = 1 * 466 + 381
466 = 4 * 85 + 41
85 = 2 * 41 + 3
41 = 13 * 3 + 2
3 = 1 * 2 + 1
2 = 1 * 1

  
thus the hcf of 847 and 2160 is 1.
and the given numbers are coprimes


hope it hepls u
 

Answer 2

Hi Friend,

10 , 7 , 4 , ...... , ( -62 ) are in A.P

a(FIRST TERM)  = 10

d(COMMON DIFFERENCE) = a3 - a2 = 4 - 7 = -3

last term = n th term = an = l = - 62

THEREFORE, WE WILL APPLY THE NTH TERM FORMULA

 a + ( n - 1 ) d = l



10 + ( n - 1 ) ( - 3 ) = -62

 ( n- 1 ) ( -3 ) = -62 - 10

 ( n - 1 ) ( - 3 ) = - 72

( n - 1) =  ( - 72 ) / ( - 3 )

 n - 1 = 24

 n= 24 +1 

   n = 25 

Number of terms in given A. P = n= 25 

middle term = ( n+ 1 ) /2 th term

 = (25 +1) / 2 th term

  = 26 /2  th term

   = 13 th term

iii) a = 10 , d= -3 , n= 13 

     a13 = ?

     a13 = a + 12d
       
            = 10 + 12 × ( -3 )

            = 10 - 36

            = -26 

 Middle term in given in A. P = a 13 = -26