Question

please solve quick the following problem quick

Answer 1

HELLO DEAR,



let the first term of AP be A and common difference be d.

the first p terms is

$a_{p} = (A + (p - 1)d = a - - - - - - (1)$




the first q term is

$a_{q} = (A + (q - 1)d = b - - - - - (2)$



the first r term is

$a_{r} = (A + (r - 1)d = c - - - - - (3)$


adding the Equation--(1) , --(2) , & --(3)
multiply by (q - r) in--(1) , (r - p) in -(2) & (p - q) in -(3)

we get,


a(q - r) + b(r - p) + c(p - q) = [A + (p - 1)d](q - r) + [A + (q - 1)d](r - p) + [A + ( p - 1)d](p - q)


=> ą(ʠ -ŗ) + ɓ(ŗ - p) + ç(p - ʠ) = Ą(ʠ - ŗ + ŗ - p + p - ʠ) + d [ (P - 1)(ʠ - ŗ) + (ʠ - 1)(ŗ - p) + (ʀ - 1)(p - ʠ)


=> ą(ʠ -ŗ) + ɓ(ŗ - p) + ç(p - ʠ) = ᴀ(0) + ᴅ( ᴘǫ - ᴘʀ - ǫ + ʀ + Ǫʀ - ᴘǫ - ʀ + ᴘ + ᴘʀ - ǫʀ - ᴘ + ǫ)

=> ą(ʠ -ŗ) + ɓ(ŗ - p) + ç(p - ʠ) = 0 + ᴅ(0)


=> ą(ʠ -ŗ) + ɓ(ŗ - p) + ç(p - ʠ) = 0


ɪ ʜᴏᴘᴇ ɪᴛs ʜᴇʟᴘ ʏᴏᴜ ᴅᴇᴀʀ,
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