Sequences and Series
nA.M.s are inserted between 2 and 100 then sum of the A.M′s is
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The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
For the following AP's, write the first term and the common difference:(i) 3,1,−1,−3,…(ii) −5,−1,3,7,…(iii) 31,35,39,311……(iv) 0.6,1.7,2.8,3.9,…
If a−bxa+bx=b−cxb+cx=c−dxc+dx(x=0),then show that a, b, c and d are in G.P.
Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?
If p, q, r are in G.P. and the equations, px2+2qx+r=0and dx2+2ex+f=0have a common root, then show that pd,qe,rfare in A.P.
Find the sum to n terms of the series :1×2+2×3+3×4+4×5+......
Find the sum of first n
terms of the following series:5+11+19+29+41+˙
If the sum of n terms of an A.P. is nP+21n(n−1)Q,where P and Q are constants, find the common difference.