# \[

{\text{Which term of the }}A.P.\;3,15,27,39,....{\text{will be }}120{\text{ }}{\text{more than its }}{21^{st}}{\text{term}}?

\]

Answer

Verified

368.7k+ 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{.}} \\

\]

Last updated date: 26th Sep 2023

â€¢

Total views: 368.7k

â€¢

Views today: 10.68k

Recently Updated Pages

What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Drive an expression for the electric field due to an class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What is the past tense of read class 10 english CBSE