Let tn be the nth term of an A-P- If -r-11099 a2r- 10100 and -r-11099 a2r-1-1099- then the common difference of A-P- is

Let $a_{n}$ be the $n^{t h}$ term of an AP. If $Σ_{r = 1}^{50} a_{2 r} = α$ and $Σ_{r = 1}^{50} a_{2 r - 1} = β$ , then what is the common difference of the A.P.

Q. If

t_{n}

, represents

n^{t h}

term of an A.P.,

t_{2} + t_{5} - t_{3} = 10

and

t_{2} + t_{9} = 17

, then find its first term and its common difference.

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Let tn be the nth term of an A.P. If 1099∑r=1a2r=10100 and 1099∑r=1a2r−1=1099, then the common difference of A.P. is

The correct option is D 91099∑r=1a2r=1099∑r=1(a2r−1+d)=1099∑r=1a2r−1+(1099)dor 10100=1099+1099.d∴ 10-1 = d or d= 9

Let $t_{n}$ be the nth term of an A.P. If $10^{99} \sum r = 1 a_{2 r} = 10^{100}$ and $10^{99} \sum r = 1 a_{2 r - 1} = 10^{99}$ , then the common difference of A.P. is

The correct option is D 9
$10^{99} \sum r = 1 a_{2 r} = 10^{99} \sum r = 1 (a_{2 r - 1} + d) = 10^{99} \sum r = 1 a_{2 r - 1} + (10^{99}) d$
or $10^{100} = 10^{99} + 10^{99} . d$
$∴$ 10-1 = d or d= 9