Question

The value of x for which 2x, (x +10) and (3x + 2) are the three consecutive terms
of an AP, is
°0820
(b) -6
(c) 18"TE 50 (d) -18
(a) 6​

Answer 1

Answer :-

Value of x should be 6 .

Note :-

• Numbers are said to be in AP , if a constant number is added to form the next term.

• The nth term of an AP is given by a + (n-1)d.

• Sum of n terms of a AP is given by n/2 [ 2a + (n-1)d]

• Arthemetic mean of two numbers is given by (a+b)/2 .

Explanation :-

Let us say that a = 2x , b = x + 10 and c = 3x + 2 .

Let the common difference of the Arthemetic Progression be k . So , if we subtract a from b , and b from c , the difference will be constant that is k .

$=> b - a = k\\ => x + 10 - 2x = k \\=> -x + 10 = k \\\bf => k + x = 10$

Also ,

$=> c - b = k\\=> 3x +2 - (x+10) = k \\=> 3x + 2-x-10=k\\=> 2x-8 = k\\\bf => 2x -k = 8$

Adding them ,

$=> k + x + 2x - k = 10 + 8 \\=> 3x = 18 \\=> x =\dfrac{18}{3}\\\bf => x = 6 .$