IIT JEE , AIEEE Forum - Mathematics , Algebra - Shortcuts to tackle level 1 "progression" problems

Avinash_Bhat

TO ALL MY DEAR FRIENDS..........

In an infinite G.P. if any one term is equal to 'n' times the sum of all the

terms following it, then the common ratio is : 1 / (n+1).

For a G.P., the sum of the products of 'n' terms taken two by two is:

r / (r+1) S_(n-1)S_n

The sum of the products of first 'n' natural no.s taken two by two is:

(n-1) n (n+1) (3n+2) / 24

If a, b, c in A.P. and a, mb, c in G.P. then: a, m²b, c in H.P.

Avinash_Bhat

(Sum of next n terms) / (Sum of first n terms) = (r)ⁿ for a G.P.

S1 > Sum to infinity of a G.P.

S2 > Sum to infinity of the squares of the terms.

Then : First term is (2*S1*S2) / (S1² + S2)

For a G.P. with an even no. of terms,

(Sum of terms occupying even places) / (Sum of terms occupying odd places)

=

Common ratio

Sum of first 'n' terms; Sum of next 'n' terms; Sum of again the next 'n' terms

of an A.P. are in A.P.

Avinash_Bhat

If a, b, c in A.P. and b, c, a in G.P. then: c, a, b in H.P.

Can this be true? Yes...just consider

a = 4

b = 1

c = -2 satisfied, kya ??

If sum to n terms of an A.P. is : an² + bn , then the sum of the next n terms of this A.P. is 3an² + bn.

Now some familiars:

a, b, c in A.P. b, c, d in G.P. c, d, e in H.P then : a, c, e in G.P.

a, b, c in A.P. b, c, d in H.P. c, d, e in A.P then : a, c, e in G.P.

a, b, c in G.P. b²,c²,d² in A.P. c, d, e in G.P then : a, c, e in A.P.

If a, b, c in G.P. then : (a+b), (b+b), (c+b) in H.P.

YOU MAY ALSO LOOK INTO OUR FRIEND Chimanshu'S TIPS, WHICH HE HAD CREATED UNDER THE TOPIC "A.P., G.P., H.P. nt difficult"

Thathwamasi