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Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that `a/p(q-r)+b/q (r-p) +c/r (p-q)=0`

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The sum of first p,q and r terms of an AP are a,b and c respectively . Show that (a)/p(q-r)+b/q(r-p)+c/r(p-q)=0

If pth,qth and rth terms of an A.P. are a, b, c respectively, then show that a(q-r)+b(r-p)+c(p-q)=0

The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectively. Show that (q-r) a+(r-p) b+(p-q)c = 0

If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and c, respectively. Prove that a^(q – r) b^(r-p) c^(P - q) = 1.

Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : If pth and rth terms of an AP are a,b and c respectively. then a(q-r)+b(r-p)+c(p-q)

If the p th and qth terms of a GP are q and p respectively, then show that its (p+ q) th term is ((q^(p))/(p^(q)))^((1)/(p-q))

If p^(th),q^(th)and r^(th) tern of G.P are a,b and c respectively then |{:(loga,p,1),(logb,q,1),(logc,r,1):}|=0

If a,b,c are respectively the p^(th), q^(th) and r^(th) terms of the given G.P. then show that (q - r) log a + (r - p) logb + (p - q) log c = 0, where a, b, c gt 0

If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

Let a,b,c,d be positive real numbers with altbltcltd . Given that a,b,c,d are the first four terms of an AP and a,b,d are in GP. The value of (ad)/(bc) is (p)/(q) , where p and q are prime numbers, then the value of q is

NCERT GUJARATI-SEQUENCES AND SERIES-EXERCISE 9.2
  1. Find the sum of odd integers from 1 to 2001.

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  2. Find the sum of all natural numbers lying between 100 and 1000, which ...

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  3. In an A.P., the first term is 2 and the sum of the first five terms is...

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  4. How many terms of the A.P. – 6, , - (11)/2 , -5 ......... are needed t...

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  5. If the pth term of an AP is 1/q and the qth term is 1/p , show that th...

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  6. If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 1...

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  7. Find the sum to n terms of the A.P., whose k^("th") term is 5k + 1.

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  8. If the sum of n terms of an A.P. is (pn + qn^2) , where p and q are co...

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  9. Answer each question by selecting the proper alternative from those gi...

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  10. If the sum of first p terms of an A.P. is equal to the sum of the firs...

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  11. Sum of the first p, q and r terms of an A.P. are a, b and c, respectiv...

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  12. The ratio of sums of m and n terms of an Ap is m^(2):n^(2). The ratio ...

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  13. If the sum of n terms of an A.P. is 3n^2 + 5n and its m^("th") term ...

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  14. Insert five numbers between 8 and 26 such that the resulting sequence ...

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  15. If (a^(n)+b^n)/ (a^(n-1) +b^(n-1)) is the A.M. between a and b, then f...

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  16. Between 1 and 31, m numbers have been inserted in such a way that the ...

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  17. A man starts repaying a loan as first instalment of Rs. 100. If he inc...

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  18. The difference between any two consecutive interior angles of a polygo...

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