Question

if the 1st term of an H.P. is 'a' and the 2nd term is b; ​

Answer 1

Answer:

then what

Step-by-step explanation:

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Answer 2

Answer:

For the A.P., 1st term =p, nth term =q

q=p+(n−1)d, where d is the common difference

⇒d= (n−1q−p

(r−1)th term of the A.P. =p+

(n−1)r(q−p) = (n−1)p(n−1)+r(q−p) ...(1)

For H.P. 1st term =p, nth term =q

⇒ the corresponding A.P. has the first term p1

and the nth term q1

q1 = p1 +(n+1)D,

whre D is the common difference

⇒D= (n−1)q1 − p1 = pq(n−1)(p−q)(n−r)th

term of the corresponding A.P.

= p1 + pq(n−1) (n−r−1)(p−q) = pq(n−1)

q(n−1)+(n−r−1)(p−q)=

pq(n−1)(n−r−1)p+q =

pq(n−1)

p(n−1)+r(q−p)

Therefore. The (n−rth term of the H.P. =

p(n−1)+r(q−p)

pq(n−1).(2)

From (1) and (2) we see that the product of the terms =pq independent of r

Step-by-step explanation:

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