Answer
Verified
431.7k+ views
\[
{\text{As we know that the given A}}{\text{.P is }} \\
\Rightarrow A.P:\;3,15,27,39,.... \\
{\text{Common difference}},\;d = {\text{difference of any two consecutive terms}} = 15 - 3 = 12. \\
{\text{As we know that the }}{n^{th}}{\text{ term of the A}}{\text{.P is given by }}{t_n}. \\
\Rightarrow {\text{So, }}{t_n} = a + (n - 1) \times d{\text{ ,}}\;{\text{where}}\;a = 3,d = 12{\text{ (1)}} \\
{\text{Hence first we have to find the value of }}{21^{st}}{\text{ term of the given A}}{\text{.P}}{\text{.}} \\
\therefore {\text{ }}{t_{21}} = 3 + (21 - 1) \times 12\; \\
{\text{ }} = 3 + 20 \times 12\;{\text{ }}\; \\
{\text{ }} = 3 + 240 \\
\Rightarrow \therefore {\text{ }}{t_{21}} = 243 \\
{\text{Let the term will be }}{m^{th}}{\text{ which is }}120{\text{ greater than its }}{21^{st}}{\text{ term }} \\
{\text{So, according to equation 1}} \\
{\text{So, }}{t_m} = 3 + (m - 1) \times 12\; \\
\Rightarrow {\text{ }}{t_m} = 12m - 9\;{\text{ (2)}}\; \\
{\text{And it is given that }}{t_m} = 120 + {t_{21}}{\text{ (3)}} \\
{\text{So, on comparing equation }}2{\text{ }}and{\text{ }}3{\text{ and putting the value of }}{t_{21}}{\text{ in it }}{\text{we get}}, \\
\Rightarrow 12m - 9 = 120 + 243 = 363 \\
\Rightarrow m = \dfrac{{372}}{{12}} = 31 \\
{\text{Hence, }}{31^{st}}{\text{ term of the given A}}{\text{.P is 120 more than its 2}}{1^{st}} \\
{\text{NOTE: - Whenever you came up with this type of problem them best way is to to compute}} \\
{\text{the given term of that A}}{\text{.P whose relation is given in the question and then compare that with}} \\
{\text{required condition}}{\text{.}} \\
\]
{\text{As we know that the given A}}{\text{.P is }} \\
\Rightarrow A.P:\;3,15,27,39,.... \\
{\text{Common difference}},\;d = {\text{difference of any two consecutive terms}} = 15 - 3 = 12. \\
{\text{As we know that the }}{n^{th}}{\text{ term of the A}}{\text{.P is given by }}{t_n}. \\
\Rightarrow {\text{So, }}{t_n} = a + (n - 1) \times d{\text{ ,}}\;{\text{where}}\;a = 3,d = 12{\text{ (1)}} \\
{\text{Hence first we have to find the value of }}{21^{st}}{\text{ term of the given A}}{\text{.P}}{\text{.}} \\
\therefore {\text{ }}{t_{21}} = 3 + (21 - 1) \times 12\; \\
{\text{ }} = 3 + 20 \times 12\;{\text{ }}\; \\
{\text{ }} = 3 + 240 \\
\Rightarrow \therefore {\text{ }}{t_{21}} = 243 \\
{\text{Let the term will be }}{m^{th}}{\text{ which is }}120{\text{ greater than its }}{21^{st}}{\text{ term }} \\
{\text{So, according to equation 1}} \\
{\text{So, }}{t_m} = 3 + (m - 1) \times 12\; \\
\Rightarrow {\text{ }}{t_m} = 12m - 9\;{\text{ (2)}}\; \\
{\text{And it is given that }}{t_m} = 120 + {t_{21}}{\text{ (3)}} \\
{\text{So, on comparing equation }}2{\text{ }}and{\text{ }}3{\text{ and putting the value of }}{t_{21}}{\text{ in it }}{\text{we get}}, \\
\Rightarrow 12m - 9 = 120 + 243 = 363 \\
\Rightarrow m = \dfrac{{372}}{{12}} = 31 \\
{\text{Hence, }}{31^{st}}{\text{ term of the given A}}{\text{.P is 120 more than its 2}}{1^{st}} \\
{\text{NOTE: - Whenever you came up with this type of problem them best way is to to compute}} \\
{\text{the given term of that A}}{\text{.P whose relation is given in the question and then compare that with}} \\
{\text{required condition}}{\text{.}} \\
\]
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE