Answer
Verified
481.5k+ views
(Hint: Use the formula of sum of first n terms of A.P. and find first term of A.P. with the help of sum of n terms of A.P.)
The sum of terms is given as,
\[{S_m} = 4{m^2} - m{\text{ }}...{\text{(1)}}\]
Let \[{a_n}\] be \[{n^{th}}\] the term of A.P., then we get,
\[{a_1} = {S_1} = 4{(1)^2} - 1 = 4 - 1 = 3\]
Now, we know that,
\[{S_n} = \dfrac{n}{2}(a + {a_n}){\text{ }}...{\text{(2)}}\]
Also, the value of \[{a_n}\] is given as
\[{a_n} = 107\]
Using the equations and, we get,
\[{S_n} = 4{n^2} - n = \dfrac{n}{2}({a_1} + {a_n})\]
\[4n - 1 = \left( {\dfrac{{3 + 107}}{2}} \right)\]
\[4n - 1 = 55\]
\[n = \dfrac{{56}}{4}\]
\[ \Rightarrow n = 14\]
So, the required solution is \[n = 14\].
Note: In order to solve these types of questions, the first term needs to be calculated first so that the formula for calculating the \[{n^{th}}\]term or the sum, can be applied.
The sum of terms is given as,
\[{S_m} = 4{m^2} - m{\text{ }}...{\text{(1)}}\]
Let \[{a_n}\] be \[{n^{th}}\] the term of A.P., then we get,
\[{a_1} = {S_1} = 4{(1)^2} - 1 = 4 - 1 = 3\]
Now, we know that,
\[{S_n} = \dfrac{n}{2}(a + {a_n}){\text{ }}...{\text{(2)}}\]
Also, the value of \[{a_n}\] is given as
\[{a_n} = 107\]
Using the equations and, we get,
\[{S_n} = 4{n^2} - n = \dfrac{n}{2}({a_1} + {a_n})\]
\[4n - 1 = \left( {\dfrac{{3 + 107}}{2}} \right)\]
\[4n - 1 = 55\]
\[n = \dfrac{{56}}{4}\]
\[ \Rightarrow n = 14\]
So, the required solution is \[n = 14\].
Note: In order to solve these types of questions, the first term needs to be calculated first so that the formula for calculating the \[{n^{th}}\]term or the sum, can be applied.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
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
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE