If every even term of a series is a time...

If every even term of a series is a times the term before it and every odd term is c times the before it, the first term being unity, then the sum to 2n terms is

`((1-a)(1-c^n a^n))/(1-ca)`

`((1-a)(1-c^(n-1) a^(n-1)))/(1-ca)`

`((1-a)(1-c^(n-2)a^(n-2)))/(1-ca)`

`((1+a)(1-c^n a^n))/(1-ca) `

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise LEVEL-2|34 Videos
SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos
SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos
REVISION TEST-2 JEE
VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos
STRAIGHT LINES
VMC MODULES ENGLISH|Exercise JEE Advanced Archive (State true or false: Q. 42)|1 Videos

Similar Questions

Explore conceptually related problems

Find the sum of 2n terms of the series whose every even term is ' a ' times the term before it and every odd term is ' c ' times the term before it, the first term being unity.

The sum of 20 terms of a series of which every even term is 2 times the term before it, every odd term is 3 times the term before it, the first term being unity is a. (2/7)(6^(10)-1) b. (3/7)(6^(10)-1) c. (3/5)(6^(10)-1) d. none of these

The nth term of a series is 3^n + 2n ; find the sum of first n terms of the series.

If S is the sum to infinite terms of a G.P whose first term is 'a', then the sum of the first n terms is

If the first term of an infinite G.P. is 1 and each term is twice the sum of the succeeding terms, then the sum of the series is

The first term of a sequence is 1, the second is 2 and every term is the sum of the two preceding terms.The n^(th) term is.

In an A.P. the third term is four times the first term, and the sixth term is 17 , find the series.

If every term of a G.P with positive terms is the sum of its two previous terms, then the common ratio of the G.P is

The 5th term of an A.P. is three times the first term. Prove that its 7th term will be two times the 3rd term.

A series whose n^(th) term is (n/x) , then sum of r terms will be

VMC MODULES ENGLISH-SEQUENCE AND SERIES -LEVEL-1

if r>1 and x=a+a/r+a/r^2+...............oo , y=b-b/r+b/r^2-..............
Text Solution
|
The odd value of n for which 704+1/2(704)+… upto n terms = 1984-1/2(1...
Text Solution
|
If every even term of a series is a times the term before it and every...
Text Solution
|
If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.
Text Solution
|
If a ,b ,c are in G.P. and x ,y are the arithmetic means of a ,ba n db...
Text Solution
|
If ai > 0 for i=1,2,…., n and a1 a2 … a(n=1) , then minimum value o...
Text Solution
|
Suppose a,b, c are in A.P. and a^(2) , b^(2),c^(2) are in G.P. if a lt...
Text Solution
|
One side of a equilateral triangle is 24 cm. The mid-points of its sid...
Text Solution
|
The sum to infinity of the series 1+2(1-(1)/(n))+3(1-(1)/(n))^(2)+ ....
Text Solution
|
Let an be the nth term of a G.P. of positive numbers. Let sum(n=1)^(10...
Text Solution
|
The sum of the series (1 2/3)^(2) + (2 1/3)^(2) + 3^2 + (3 2/3)^(2) ...
Text Solution
|
The roots of equation x^2+2(a-3)x+9=0 lie between -6 and 1 and 2, h1, ...
Text Solution
|
If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab...
Text Solution
|
The number a, b and c are between 2 and 18, such that (i) their su...
Text Solution
|
three number a,b,c are in GP such that : (i) a+b+c=70 (ii) 4a,5b,4c a...
Text Solution
|
If tr denotes the r^(th) term of an G.P. and t1 t5 t10 t16 t21 t25 ...
Text Solution
|
The summation of series sum(r=1->99) 1/(sqrt(r+1)+sqrtr) is:
Text Solution
|
If a,b,c are in A.P. then the roots of the equation (a+b-c)x^2 + (b-a...
Text Solution
|
If sum of first n terms of a series is n/(n+1) find 1/(T8)where T8 is ...
Text Solution
|
if (1+3+5+7+....(2p-1))+(1+3+5+...+(2q-1)) =1+3+5+...+(2r -1), then le...
Text Solution
|