Home
Class 12
MATHS
Let an be the n^(t h) term of an A.P. If...

Let `a_n` be the `n^(t h)` term of an A.P. If `sum_(r=1)^(100)a_(2r)=alpha&sum_(r=1)^(100)a_(2r-1)=beta,` then the common difference of the A.P. is (a)`alpha-beta` (b) `beta-alpha` (c)`(alpha-beta)/2` (d) None of these

Text Solution

AI Generated Solution

To find the common difference of the arithmetic progression (A.P.) given the sums of even and odd indexed terms, we can follow these steps: ### Step 1: Define the nth term of the A.P. Let the first term of the A.P. be \( a \) and the common difference be \( d \). The nth term of the A.P. can be expressed as: \[ a_n = a + (n-1)d \] ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Let a_(n) be the nth term of an AP, if sum_(r=1)^(100)a_(2r)=alpha " and "sum_(r=1)^(100)a_(2r-1)=beta , then the common difference of the AP is

Let a_(n) be the n^(th) term of an A.P.If sum_(r=1)^(100)a_(2r)=alpha&sum_(r=1)^(100)a_(2r-1)=beta, then the common difference of the A.P.is alpha-beta(b)beta-alpha(alpha-beta)/(2)quad (d) None of these

Let a_(n) be the nth term of a G.P.of positive numbers.Let sum_(n=1)^(100)a_(2n)=alpha and sum_(n=1)^(100)a_(2n-1)=beta, such that alpha!=beta, then the common ratio is alpha/ beta b.beta/ alpha c.sqrt(alpha/ beta) d.sqrt(beta/ alpha)

If sum_(r=1)^9 ((r+3)/2^r)(.^9C_r)=alpha(3/2)^9+beta , then alpha+beta is equal to :

If A_alpha=[cosalphasinalpha-sinalphacosalpha],t h e nA_alphaA_beta= (a)A_(alpha+beta) (b) A_(alphabeta) (c) A_(alpha-beta) (D) None of these

Sum of n terms of the series sinalpha-sin(alpha+beta)+sin(alpha+2beta)-sin(alpha+3beta)+….

If tan alpha=(1-cos beta)/(sin beta), then a )tan3 alpha=tan2 beta(b)tan2 alpha=tan beta(c)tan2 beta=tan alpha(d) none of these