Sequences and Series
If there are 3A.M′s between 4 and 84, find their sum.
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then find r=2∑∞T1˙
Show that the sequence 9, 12, 15, 18, ... is an A.P. Find its 16th term and the general term.
Prove that (6666)2+(8888)=44444.
The sum of three numbers in GP. Is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.
The A.M. and H.M. between two numbers are 27 and 122, respectively, then find their G.M.
Find the value of n so that an+bnan+1+bn+1 may be the geometric mean between a and b.
The pth term of an A.P. is a and qth term is b˙ Then find the sum of its (p+q) terms.
Insert four H.M.’s between 2/3 and 2/13.