Question

The solution of the equation(x+1)+(x+4)+(x+7)+.........+(x+28)=155
is
A) 1 B) 2 C) 3 D) 4

Answer 1

Hi ,

case 1 :

Take ,

1 , 4 , 7 , .... 28 are in A.P

first term = a = 1

common difference = a2 - a1

d = 4 - 1 = 3

nth term = an = 28

a + ( n - 1 )d = 28

1 + ( n - 1 ) 3 = 28

( n - 1 ) 3 = 28 - 1

n - 1 = 27/3

n = 9 + 1

n = 10 ,

case 2 :

sum of n terms = Sn = n/2 [ a + an ]

Here ,

a = 1 , n = 10

S10 = 10/2 [ 1 + 28 ]

= 5 × 29

= 145 ---( 1 )

Now ,

( x + 1 ) + ( x + 4 ) + ..+ ( x + 28 ) = 155

[ ( x + x + ....+ 10 terms ) + ( 1 + 4 +..+ 28 ) ] = 155

10x + 145 = 155

10x = 155 - 145

10x = 10

x = 10/10

x = 1

Therefore ,

Option ( A ) is correct.

I hope this helps you.

: )