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If `S_5 = 15` and `S_6 = 21`, Find `T_6`. - Algebra

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प्रश्न

If `S_5 = 15` and `S_6 = 21`, Find `t_6`.

उत्तर

`S_(n+1) -  S_n = t_(n+1)`

`t_6 = S_6 - S_5 =  21 - 15 = 6`

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2017-2018 (March) Set A

संबंधित प्रश्‍न

State whether the following sequence is an AP or not: 1, 3, 6, 10………


If the nth term of a progression be a linear expression in n, then prove that this progression is an AP


Write first four terms of the A.P. when the first term a and the common differenced are given as follows:

 a = 10, d = 10


Write the first three terms in the sequences defined by the following

an = n2  + 1


Find the common difference and write the next four terms of each of the following arithmetic progressions:

1, −2, −5, −8, ...


Find a30 − a20 for the A.P.

−9, −14, −19, −24, ...


Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

20th term is 10 more than the 18th term.


If an A.P. consists of n terms with first term a and nth term show that the sum of the mth term from the beginning and the mth term from the end is (a + l).


Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ...


Define an arithmetic progression.

 

First term a and common difference d are given below. Find the corresponding A.P.

a = 5, d = 6


The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.


Choose the correct alternative answer for the following sub question

In an A.P., 0, – 4, – 8, – 12, ... find t2 = ?


Find 27th and nth term of given A.P. 5, 2, – 1, – 4, ......


If the common difference of an AP is 3, then a20 - a15 is ______.


Which of the following form an AP? Justify your answer.

–1, –1, –1, –1,...


Which of the following form an AP? Justify your answer.

11, 22, 33,...


In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers

The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10% per annum.


The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15th term.


Case Study

Push-ups are a fast and effective exercise for building strength. These are helpful in almost all sports including athletics. While the push-up primarily targets the muscles of the chest, arms, and shoulders, support required from other muscles helps in toning up the whole body.


Nitesh wants to participate in the push-up challenge. He can currently make 3000 push-ups in one hour. But he wants to achieve a target of 3900 push-ups in 1 hour for which he practices regularly. With each day of practice, he is able to make 5 more push-ups in one hour as compared to the previous day. If on first day of practice he makes 3000 push-ups and continues to practice regularly till his target is achieved. Keeping the above situation in mind answer the following questions:

  1. Form an A.P representing the number of push-ups per day and hence find the minimum number of days he needs to practice before the day his goal is accomplished?
  2. Find the total number of push-ups performed by Nitesh up to the day his goal is achieved.

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