Question

How many terms are there in this A.p ?

1,3,5,7,..........,99​

Answer 1

$\huge\sf{ \underline{ \underline{Given}}}$

• a = 1
• d = 2
• $\sf{\ a_{n}}$ = 99

$\huge\sf{ \underline{ \underline{To \: Find}}}$

• No. of terms (n)

$\huge\sf{ \underline{ \underline{Concept\:Used}}}$

$\sf{ \boxed{\ a_{n} = a+(n-1)d}}$

$\huge\sf{ \underline{ \underline{Solution }}}$

$\sf{\ a_{n}\:=\:a+(n-1)d}$

$\bf{Put \:value \:in\: Formula}$

$\sf{99\:=\:1+(n-1)2}$

$\sf{99-1\:=\:2(n-1)}$

$\sf{\dfrac{98}{2}\:=\:(n-1)}$

$\sf{\dfrac{\cancel{98}}{\cancel{2}}\:=\:(n-1)}$

$\sf{49\:=\:n-1 }$

$\sf{n\:=\:50 }$

Answer 2

$\Large{\underline{\underline{\bf{Given:-}}}}$

$\rm{a_1=1}$

$\rm{d=\: a_2-a_1\:= \: 3-1\:=\:2}$

$\rm{a_n=99}$

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$\Large{\underline{\underline{\bf{To\: Find:-}}}}$

$\rm{How\: many\: terms \:are \:there \:in \:this \:A.p\: ? }$

$\rm{n=?}$

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$\Large{\underline{\underline{\bf{Formula\: used:-}}}}$

$\rm{a_n=a+(n-1)d}$

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$\Large{\underline{\underline{\bf{Solution:-}}}}$

$\rm{a_n=a+(n-1)d}$

${\bold{\underline{\underline{Put\: values \: in \: this \: formula}}}}$

⟹$\rm{99=1+(n-1)d}$

⟹$\rm{99=1+2n-2}$

⟹$\rm{99+2-1=2n}$

⟹$\rm{100=2n}$

⟹$\rm{\frac{100}{2}=n}$

⟹$\rm{50=n}$

${\boxed{\boxed{\rm{n=50}}}}$

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$\Large{\underline{\underline{\bf{Thanks}}}}$