Answer
424.5k+ views
Hint: Notice that the terms of the series given in the question are in arithmetic progression with common difference and the first term equal to 5 and 2, respectively. So, directly use the formula of sum of an A.P. to get the answer. The sum of first r terms of an AP is given by $ {{S}_{r}}=\dfrac{r}{2}\left( 2a+\left( r-1 \right)d \right) $ , where a is the first term and d is the common difference of the AP.
Complete step-by-step answer:
Before starting with the solution, let us discuss what an A.P. is. A.P. stands for arithmetic progression and is defined as a sequence of numbers for which the difference of two consecutive terms is constant. The general term of an arithmetic progression is denoted by $ {{T}_{r}} $ , and sum till r terms is denoted by $ {{S}_{r}} $ .
$ {{T}_{r}}=a+\left( r-1 \right)d $
$ {{S}_{r}}=\dfrac{r}{2}\left( 2a+\left( r-1 \right)d \right)=\dfrac{r}{2}\left( a+l \right) $
Now moving to the series given in the question. We can see that the terms of the series given in the question are in A.P. with common difference equal to 5 and the first term of the A.P. being 2.
Now to find the sum of the A.P., we will use the formula $ {{S}_{r}}=\dfrac{r}{2}\left( 2a+\left( r-1 \right)d \right) $ . In the formula a is the first term, so a=2 and d is the common difference, d=5. Therefore, the sum of the series 2, 7, 12….… to 10 terms is:
$ {{S}_{r}}=\dfrac{r}{2}\left( 2a+\left( r-1 \right)d \right) $
$ \Rightarrow {{S}_{r}}=\dfrac{10}{2}\left( 2\times 2+5\left( 10-1 \right) \right) $
$ \Rightarrow {{S}_{r}}=5\left( 4+5\times 9 \right) $
$ \Rightarrow {{S}_{r}}=5\times 49=245 $
So, the correct answer is “Option B”.
Note: It is not always necessary that you can notice that the sequences are in the form of simple arithmetic progressions and draw results, but it is for sure that the terms of a sequence will have some order, and it depends on you how wisely you figure out the pattern. The suggested approach can be to try to find the general term of the sequence by observing the pattern of numbers appearing in the sequence and proceed. For the above question if you don’t know the formula of sum of r terms of the AP, you can directly add the 10 consecutive terms to get the answer.
Complete step-by-step answer:
Before starting with the solution, let us discuss what an A.P. is. A.P. stands for arithmetic progression and is defined as a sequence of numbers for which the difference of two consecutive terms is constant. The general term of an arithmetic progression is denoted by $ {{T}_{r}} $ , and sum till r terms is denoted by $ {{S}_{r}} $ .
$ {{T}_{r}}=a+\left( r-1 \right)d $
$ {{S}_{r}}=\dfrac{r}{2}\left( 2a+\left( r-1 \right)d \right)=\dfrac{r}{2}\left( a+l \right) $
Now moving to the series given in the question. We can see that the terms of the series given in the question are in A.P. with common difference equal to 5 and the first term of the A.P. being 2.
Now to find the sum of the A.P., we will use the formula $ {{S}_{r}}=\dfrac{r}{2}\left( 2a+\left( r-1 \right)d \right) $ . In the formula a is the first term, so a=2 and d is the common difference, d=5. Therefore, the sum of the series 2, 7, 12….… to 10 terms is:
$ {{S}_{r}}=\dfrac{r}{2}\left( 2a+\left( r-1 \right)d \right) $
$ \Rightarrow {{S}_{r}}=\dfrac{10}{2}\left( 2\times 2+5\left( 10-1 \right) \right) $
$ \Rightarrow {{S}_{r}}=5\left( 4+5\times 9 \right) $
$ \Rightarrow {{S}_{r}}=5\times 49=245 $
So, the correct answer is “Option B”.
Note: It is not always necessary that you can notice that the sequences are in the form of simple arithmetic progressions and draw results, but it is for sure that the terms of a sequence will have some order, and it depends on you how wisely you figure out the pattern. The suggested approach can be to try to find the general term of the sequence by observing the pattern of numbers appearing in the sequence and proceed. For the above question if you don’t know the formula of sum of r terms of the AP, you can directly add the 10 consecutive terms to get the answer.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)