Sequences and Series
Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than $$200$$ and less than $$220$$. If the second term in it is $$12$$, then $$4^{th}$$ term is :
$$\displaystyle{ a }_{ n }=4n-3;{ a }_{ 17 },{ a }_{ 24 }$$
We have $$a_n = 4n-3$$
For $$a_{17}, n=17$$
$$\displaystyle\therefore { a }_{ 17
}=4(17)-3=68-3=65$$
and for $$a_{24}, n=24$$
$${
a }_{ 24 }=4(24)-3=96-3=93$$
Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than $$200$$ and less than $$220$$. If the second term in it is $$12$$, then $$4^{th}$$ term is :
Let X be the set consisting of the first $$2018$$ terms of the arithmetic progression $$1, 6, 11,$$______, and Y be the set consisting of the first $$2018$$ terms of the arithmetic progression $$9, 16, 23$$, ________. Then, the number of elements in the set X$$\cup$$Y is _______?
$$\displaystyle { a }_{ n }=n(n+2)$$
$$\displaystyle { a }_{ n }=\frac { n }{ n+1 } $$
$$\displaystyle{ a }_{ n }={ 2 }^{ n }$$
$$\displaystyle{ a }_{ n }=\frac { 2n-3 }{ 6 } $$
$$\displaystyle{ a }_{ n }={ (-1) }^{ n-1 }\quad { 5 }^{ n+1 }$$
$$\displaystyle{ a }_{ n }=n\frac { { n }^{ 2 }+5 }{ 4 } $$
$$\displaystyle { a }_{ n }=\frac { { n }^{ 2 } }{ { 2 }^{ n } } ;{ a }_{ 7 }$$
$$\displaystyle{ a }_{ n }=({ -1 })^{ n-1 }{ n }^{ 3 };{ a }_{ 9 }$$