If the pth, qth and rth …
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Sia ? 6 years, 6 months ago
Let the first term and common difference of the AP be A and D
pth term = a ……… (given)
= A + (p – 1)D = a ............(1)
qth term = b
{tex}\Rightarrow {/tex} A + (q - 1) D = b ......... (2)
rth term = c .......... Given
{tex}\Rightarrow {/tex} A + (r - 1) D = c ........ (3)
Multiplying equations (1), (2) and (3) by q - r, r - p and p - q respecitvely, we get
a(q - r) + b(r - p) + c(p - q)
= [A + (p - 1) D] (q - r) + [A + (q - 1)D] (r - p) + [A + (r - 1) D] (p - q)]
= A [q - r + r - p + p - q] + D [(p - q) (q - r) + (q - 1) (r- p) + (r - 1) (p - q)]
= A (0) + D(0)
= 0
0Thank You