arithmetic
posted by kartik hans .
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l.
2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1.
3. The sum of four numbers which are in A.P is 32 and the product of whose extremes is 55. Find the numbers.
4. The angles of a quadrilateral are in A.P whose common difference is 10. Find the angles.
5. If a (1/b+1/c), b(1/c+1/b), c(1/a+1/b) are in A.P. Show that a, b, c are in A.P.
6. Evaluate 1/2 +1/3 +1/6+to 10 terms
7. Find the value of x such that 25+22+19+16++x=115
8. There are n arithmetic means between 5 and 86. Show that the ratio of the first and the last means is 2:11. Find n
9. If a, b, c are in G.P and ax=by=cz then show that 1/x+1/z=2/y
10. The second third and sixth term of an A.P are consecutive terms of G.P. Find the common ratio of G.P
11. The products of three numbers which are in G.P is 216. If 2,8,6 are added to them , the resulting numbers form an A.P. Find the numbers.
12. If a, b, c are in G.P and x, y are respectively the arithmetic means of a, b and b, c . Show that a/x + c/y=2 and 1/x+1/y=2/b.
13. The sum of first eight terms of G.P is five times the sum of the first four terms. Find the common ratio.
14. The ratio of the sum of first three terms is to that of first b terms of a G.P is 125:152. Find the common ratio.
15. Evaluate Ʃ10 k=1(2k+3k1).
16. Find the sum of geometric series: (x + y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3)+to n terms.
17. Find the sum of n terms: 5+55+555+.
18. How many terms of the series 1+4+16+64+ make the sum 5461?
19. Find the two positive numbers whose arithmetic mean is 34 and the geometric mean is 16.
20. Insert 6 geometric mean between 27and 1/81.
21. If (a1) is the G.M between (a2) and (a+1). Find a.
22. Find the two positive numbers whose difference is 12 and their A.M exceeds the G.M by 2.
23. If a is the A.M between b and c and g1, g2 are two geometric means between b and c. show that

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