Sequence, Finite sequence, Infinite sequence, Series, Progression and Arithmetic Progression
Obtain the required term from the given sequence of A.P.
(1) -6,-4,-2,…. Find 12th term (2) 1,5,9,… Find 20th term (3) 4, 7/2, 3, 5/2 … 25th term
How to find nth term of an A.P. ( Tn = a + (n-1)d )
If third term of an A.P. is 12 and sixth term is 42, find twenty sixth term.
(1) Eighth term of an A.P. is 5 and thirteenth term is 25, Find fiftieth term. (2) If nineteenth term of an A.P. is 100 and twenty-ninths term is 60, find seventieth term.
If pth term of an A.P. is q and qth term of an A.P. is p, then show that (p+q)th term is zero.
(1) Determine z so that z+2, 4z-6 and 3z-2 are the three consecutive terms of an A.P. (2) If a,b,c are in A.P. then prove that the following terms are also in A.P. (i) 1/bc, 1/ac, 1/ab (ii) b+c, c+a, a+b
If a,b,c are in A.P. then prove that (ab+ca)/bc, (bc+ab)/ca, (ca+bc)/ab are also in A.P.
If a, b, c are in A.P. then prove that (b+c)2-a2, (c+a)2-b2, (a+b)2-c2.
If a2, b2, c2 are in A.P. then prove that the followings terms are also in A.P. (i) a/bc, b/ac, c/ab (ii) 1/(b+c), 1/(a+c), 1/(a+b)
If a/(b+c), b/(c+a), c/(a+b) in A.P., prove that a2, b2, c2 are also in A.P.
