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0 votes
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in Arithmetic Progression by (31.3k points)
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In an AP, Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp + q is equal to 

A. 0 

B. –(p + q) 

C. p + q 

D. pq

1 Answer

+1 vote
by (30.9k points)
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Best answer

Correct answer is B. -(P + q)

Sp = \(\frac{p}{2}\){2A + (p–1) D} = q, given 

Sq = \(\frac{q}{2}\)(2A + (q–1) D} = p, given 

On Subtracting the second equation from 1st we get, 

D = –2\(\frac{(P+q)}{Pq}\) 

Also On adding the two equations we get,

2A + \(\frac{(P +q -2)D}{2} = \frac{p}{q} + \frac{q} {p}\)

Now

[BY substituting the value of D]

= - (P + q)

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