Sequences and Series
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The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the GP.
If a, b, c are in G.P. and ax1=by1=cz1,prove that x, y, z are in A.P.
Which term of the AP : 121, 117, 113, . . ., is its first negative term?[Hint : Find n for an<0]
Determine the AP whose 3rdterm is 5 and the 7thterm is 9.
The pth,qthand rthterms of an A.P. are a, b, c, respectively. Show that (q−r)a+(r−p)b+(p−q)c=0.
A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his one.
Write the first five terms of the sequence and obtain the corresponding series : a1=a2=2,an=an−1−1,n>2.
Let the sequence anbe defined as follows : a1=1,an=an−1+2for n≥2. Find first five terms and write corresponding series.