Class 10 Mathematics - Chapter - 1 - Examination preparation - Q3- The nth term of an arithmetic sequence is 8n - 4, prove the sum of n consecutive terms of this sequence will be a perfect square.

Question 3

The nth term of an arithmetic sequence is 8n - 4. You need to prove that the sum of n consecutive terms of this  sequence will be a perfect square. 

Class 10 Mathematics - Chapter - 1 - Examination preparation : Q2-Calculate the 15th term of this sequence where an arithmetic sequence with common difference 6 and 7th term 52

Question 2

Consider an arithmetic sequence with common difference 6 and 7th term 52. 

a Calculate the 15th term of this sequence.

b Is it possible to get a difference of 100 between any two terms of this sequence?

Class 10 Mathematics - Chapter - 1 - Examination preparation - Calculate what is the common difference and sum of the first 10 terms, Given that the 5th term and 6th term of an arithmetic sequence of 10 terms are 17 and 20 respectively

 Given that the 5th term and 6th term of an arithmetic sequence of 10 terms are 17 and 20 respectively.

a) Calculate what is the common difference? Explain with steps.

b) Calculate what is the sum of the first 10 terms ? Explain with steps?

Answer

Class-10 Mathematics-Chapter-1 Arithmetic Sequence Important points to refer

Class-10 Mathematics-Chapter-1 Arithmetic Sequence Important points 

1. A set of numbers written as the first, second, third and so on, is called a sequence.
2. The numbers forming a sequence are called its terms.
3. A sequence got by starting with any number and adding a fixed number repeatedly is called an arithmetic sequence.
4. An arithmetic sequence in which we get the same number on subtracting from any term, the term immediately preceding it.
5. This constant difference got by subtracting from any term the just previous term, is called the common difference of an arithmetic sequence.
6. The difference between any two terms of an arithmetic sequence is the product of the difference of positions and the common difference.
7. In an arithmetic sequence, term difference is proportional to position difference; and the constant of proportionality is the common difference.
8. In any arithmetic sequence of natural numbers, the difference of any two terms is a multiple of the common difference. This means they leave the same remainder on division by the common difference.
9. Any arithmetic sequence of natural numbers is of the form described first; it consists of numbers leaving the same remainder on division by a specific number. And this divisor is the common difference.
10. In an arithmetic sequence, the sum of the first five times the middle term and the sum first seven terms is seven times the middle term.
11. Any arithmetic sequence is of the form x_n =  an + b where a and b are fixed numbers; conversely, any sequence of this form is an arithmetic sequence.
12. The sum of any number of consecutive natural numbers, starting with one, is half the product the last number and the next natural number.
13. For the arithmetic sequence
    x_n = an + b
    the sum of the first n terms is
    x₁, + x₂ + ... + x_n = ½  an(n + 1) + nb
14. The sum of any number of consecutive terms of an arithmetic sequence is half the product of the number of terms and the sum of the first and last terms.