Question

sum of the first p, q, r terms of an ap are a, b, c respectively pls guys explain it briefly​

Answer 1

Answer:

let A be the first term and D be the common difference of the given A.P.

Then, a= Sum of p terms

⟹a=

2

p

{2A+(p−1)D}

⟹

p

2a

={2A+(p−1)D} ...(i)

b= Sum of q terms

⟹b=

2

q

{2A+(q−1)D}

⟹

q

2b

={2A+(q−1)D} ...(ii)

and, c= Sum of r terms

⟹c=

2

r

{2A+(r−1)D}

⟹

r

2c

={2A+(r−1)D} ...(iii)

Multiplying equation (i), (ii) and (iii) by (q−r),(r−p) and (p−q) respectively and adding, we get

p

2a

(q−r)+

q

2b

(r−p)+

r

2c

(p−q)

={2A+(p−1)D}(q−r)+{2A+(q−1)D}(r−p)+{2A+(r−1)D}(p−q)

=2A(q−r+r−p+p−q)+D{(p−1)(q−1)(r−p)+(r−1)(p−q)

=2A×0+D×0=0

Step-by-step explanation:

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