Question

Find x such that 2+x, 3+x, 5+x may be in h. p

Answer 1

Answer:

x = 1

For explaination , please refer to the attachment .

Note:

★ HP (Harmonic Progression) : A sequence is is said to be in Harmonic Progression if the reciprocal of its terms are in AP (Arithmetic Progression) .

★ If a , b , c are in AP , then 1/a , 1/b , 1/c are in HP .

★ If a , b , c are in HP , then 1/a , 1/b , 1/c are in AP .

★ The general form of AP is ;

a , a + d , a + 2d , a + 3d , . . . , a + (n-1)d

★ The general form of HP is ;

1/a , 1/(a + d) , 1/(a + 2d) , . . . , 1/[a + (n-1)d]

★ If a , b , c are in AP , then 2b = a + c .

★ If a , b , c are in HP , then 1/a , 1/b , 1/c are in AP and hence 2/b = 1/a + 1/b .

Answer 2

Answer:

+1 is the answer, +1 is required solution