Let an be the nth term of an A.P. If displaystyle∑r=1100 a2 r=α and displaystyle∑r=1100 a2 r-1=β, and the common difference of A.P. is (α-β/λ) then find λ.

Question

Let an be the nth term of an A.P. If displaystyle∑r=1100 a2 r=α and displaystyle∑r=1100 a2 r-1=β, and the common difference of A.P. is (α-β/λ) then find λ. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e55a5c72d8bd8af846fd812c9b0eef21-.png" /> 100 d=α-β d=(α-β/100)

Q. Let $a_{n}$ be the nth term of an A.P. If $r = 1 \sum 100 a_{2 r} = α$ and $r = 1 \sum 100 a_{2 r - 1} = β$ , and the common difference of A.P. is $\frac{α - β}{λ}$ then find $λ$ .

$100 d = α - β$
$d = \frac{α - β}{100}$

Q. Let an​ be the nth term of an A.P. If r=1∑100​a2r​=α and r=1∑100​a2r−1​=β, and the common difference of A.P. is λα−β​ then find λ.

100d=α−β d=100α−β​

Q. Let $a_{n}$ be the nth term of an A.P. If $r = 1 \sum 100 a_{2 r} = α$ and $r = 1 \sum 100 a_{2 r - 1} = β$ , and the common difference of A.P. is $\frac{α - β}{λ}$ then find $λ$ .

$100 d = α - β$
$d = \frac{α - β}{100}$