- Home
- Standard 11
- Mathematics
8. Sequences and Series
medium
यदि $b _{1}, b _{2}, b _{3}, \ldots b _{11}$ एक वर्धमान $A.P.$ है और इसके पदों का प्रसरण $90$ है, तो इस $A.P.$ का सार्व अन्तर है
A
$3$
B
$9$
C
$-9$
D
$-3$
(JEE MAIN-2020)
Solution
Let a be the first term and $d$ be the common
difference of the given A.P. Where $d>0$
$\overline{ X }= a +\frac{0+ d +2 d +\ldots+10 d }{11}$
$=a+5 d$
$\Rightarrow$ varience $=\frac{\Sigma\left(\bar{X}-x_{i}\right)^{2}}{11}$
$\Rightarrow 90 \times 11=\left(25 d^{2}+16 d^{2}+9 d^{2}+4 d^{2}\right) \times 2$
$\Rightarrow d =\pm 3 \Rightarrow d =3$
Standard 11
Mathematics
