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.13 Sum ofp', qth, rth terms of an arithmetic progression are a, b, c respectively, thenindprove that ​

Answer»

CORRECT QUESTION.

→ pth, qth, RTH terms of an arithmetic

progression are a, b, c RESPECTIVELY then

prove that a(q - r) + b ( r - p) + c ( p - q) = 0.

→ EXPLANATION.

→ Nth terms of an Ap

→ An = a + ( n - 1 ) d

→ pth = a + ( p - 1 ) d = a......(1)

→ qth = a + ( q - 1 ) d = b ......(2)

→ rth = a + ( r - 1 ) d = c ........(3)

→ From equation (1) and (2) we get,

→ ( p - q) d = a - b

→ ( p - q) = a - b / d .......(4)

→ From equation (2) and (3) we get,

→ ( q - r) d = b - c

→ ( q - r ) = b - c / d ........(5)

→ From equation (3) and (1) we get,

→ ( r - p) d = c - a

→ ( r - p) = c - a / d .......(6)

→ To prove.

→ a(q - r) + b ( r - p) + c ( p - q) = 0.

→ put the VALUE in this equation we get,

→ a ( b - c / d ) + b ( c - a / d) + c ( a - b / d) = 0

→ 1/d [ ab - ac + bc - ab + ca - cb ] = 0

→ 0

→ Hence proved.


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