Q2 of 167 Page 20

Mark the correct alternative in the following:

If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum or p + q terms will be


Here, Sp=q and Sq=p


i.e. and


i.e. ____(i)


and ____(ii)


Now,multiplying (i) with q and (ii) with p and then subtracting we get


pq(p-1)d-pq(q-1)d=2q2-2p2


∴pqd(p-q)=2(q2-p2)


∴ pqd(p-q)=2(p-q)(p+q)



Substituting the value of d in (i) we get,



∴ 2ap2q-2p(p-1)(p+q)=2pq2


∴ apq-(p-1)(p+q)=q2


∴ apq=q2+(p-1)(p+q)


∴ apq=q2+p2+pq-p-q



Now,




=-(p + q)

More from this chapter

All 167 →
11

If the sum of n terms of two A.P.’s are in the ratio (3n + 2) : (2n + 3), find the ratio of their 12th terms.

 1

Mark the correct alternative in the following:

If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is


 3

Mark the correct alternative in the following:

If the sum of n terms of an A.P. be 3 and its common difference is 6, then its first term is


 4

Mark the correct alternative in the following:

Sum of all two digit numbers which when divided by 4 yield unity as remainder is