Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=(-1)^{n-1} 5^{n+1}$
Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=(-1)^{n-1} 5^{n+1}$
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 $15625 .$
Similar Questions
Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$
Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$
If three numbers be in $G.P.$, then their logarithms will be in
If three numbers be in $G.P.$, then their logarithms will be in
A manufacturer reckons that the value of a machine, which costs him $Rs.$ $15625$ will depreciate each year by $20 \% .$ Find the estimated value at the end of $5$ years.
A manufacturer reckons that the value of a machine, which costs him $Rs.$ $15625$ will depreciate each year by $20 \% .$ Find the estimated value at the end of $5$ years.
The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?
The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?
- [IIT 2017]
Four numbers are in arithmetic progression. The sum of first and last term is $8$ and the product of both middle terms is $15$. The least number of the series is
Four numbers are in arithmetic progression. The sum of first and last term is $8$ and the product of both middle terms is $15$. The least number of the series is