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8. Sequences and Series
medium
अनुक्रम में प्रत्येक के प्रथम पाँच पद लिखिये, जिनका $n$ वाँ पद दिया गया है
$a_{n}=(-1)^{n-1} 5^{n+1}$
A
$25, - 125,625, - 3125,15625$
B
$25, - 125,625, - 3125,15625$
C
$25, - 125,625, - 3125,15625$
D
$25, - 125,625, - 3125,15625$
Solution
Substituting $n=1,2,3,4,5,$ we obtain
$a_{1}=(-1)^{1-1} 5^{1+1}=5^{2}=25$
$a_{2}=(-1)^{2-1} 5^{2+1}=-5^{3}=-125$
$a_{3}=(-1)^{3-1} 5^{3+1}=5^{4}=625$
$a_{4}=(-1)^{4-1} 5^{4+1}=-5^{5}=-3125$
$a^{5}=(-1)^{5-1} 5^{5+1}=5^{6}=15625$
Therefore, the required terms are $25,-125,625,-3125$ and $15625 .$
Standard 11
Mathematics
