If α =x1+x3+ ldots x199 and β =x2+x4+ ldots x200 , such that x1,x2,x3,...............x200 are in arithmetic progression, then their common difference is

Question

If α =x1+x3+ ldots x199 and β =x2+x4+ ldots x200 , such that x1,x2,x3,...............x200 are in arithmetic progression, then their common difference is (A) β -α  (B) (β - α /2) (C) (α - β /10) (D) (β - α /100)

Tardigrade Admin · Accepted Answer

In the A.P. x1, x2, x3, ldots ldots ldots .x200 let the common difference be d . ∴ α =x1+x3+ ldots ldots ldots .+x199=(100/2)(x1 + x199) =50(2 x1 + 198 d) β =x2+x4+ ldots ldots ldots x200=(100/2)(x2 + x200) = 50(x1 + d + x1 + 199 d) =50(2 x1 + 200 d) β -α =100d d=(β - α /100)

Q. If $α = x_{1} + x_{3} + \dots x_{199}$ and $β = x_{2} + x_{4} + \dots x_{200}$ , such that $x_{1}, x_{2}, x_{3}, ............... x_{200}$ are in arithmetic progression, then their common difference is

$β - α$

$\frac{β - α}{2}$

$\frac{α - β}{10}$

$\frac{β - α}{100}$

Q. If α=x1​+x3​+…x199​ and β=x2​+x4​+…x200​ , such that x1​,x2​,x3​,...............x200​ are in arithmetic progression, then their common difference is

β−α

2β−α​

10α−β​

100β−α​

In the A.P. x1​,x2​,x3​,……….x200​ let the common difference be d . ∴α=x1​+x3​+……….+x199​=2100​(x1​+x199​) =50(2x1​+198d) β=x2​+x4​+………x200​=2100​(x2​+x200​) = 50(x1​+d+x1​+199d) =50(2x1​+200d) β−α=100d d=100β−α​

Q. If $α = x_{1} + x_{3} + \dots x_{199}$ and $β = x_{2} + x_{4} + \dots x_{200}$ , such that $x_{1}, x_{2}, x_{3}, ............... x_{200}$ are in arithmetic progression, then their common difference is

$β - α$

$\frac{β - α}{2}$

$\frac{α - β}{10}$

$\frac{β - α}{100}$