Sequences, Series and Progressions

Q.

Question 1
Visualize 3.765 on the number line using successive magnification.

Q.

Look at the pattern and fill in the blanks $16,23,30,37,\_\_\_$

Q.

7th term of the sequence$\sqrt{2}$, $\sqrt{10}$, $5\sqrt{2}$….is

1. $125\sqrt{10}$

2. $25\sqrt{2}$

3. $125$

4. $125\sqrt{2}$

Q. 5, 5, 5, 5, 5, ....... is an arithmetic progression.

1. True
2. False

Q.

What is the difference between sequence and progression?

Q.

Arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is ___.

1. increasing

2. zero

3. constant

4. none of these

Q. What is finite and infinite arithmetic progression?

Q.

An arithmetic progression is defined as a sequence of numbers with a constant difference between consecutive terms.

1. True

2. False

Q.

Find the next term of the sequence $3,10,20,33,49,68,\_\_\_.$

Q.

Write the smallest number which can be shown as a line, rectangle, square and triangle.

Q.

Which of the following can be expressed as the sum of square of two positive integers, as well as three positive integers

A-75

B-192

C-250

D-100

Q.

Observe the pattern of the given series and fill in the blanks:

$2,4,6,8,\_,\_,\_$

Q. What is arithmetic progression?

Q. Find the sum of the first 30 terms of the arithmetic sequence 10, 18, 26...

Q.

Give an example for a function which is not a sequence.

Q. The $5^{th}and{8}^{th}$ terms of a G.P. are 48 and 384 respectively. Find the G.P. if terms of G.P. are real numbers.

1. 
   $0,2,10,14,...$
2. 
   $3,6,12,24,...$
3. 
   $8,20,35,40,...$
4. 
   $5,10,15,20,...$

Q. State True or False:
5, 5, 5, 5, 5, ....... is an arithmetic progression.

1. True
2. False

Q. The pattern 1, 3, 5, 7... represents numbers.

1. odd
2. even
3. whole

Q.

The sum of the first n terms of an arithmetic sequence is 2n² + 3n. find the algebraic form of this sequence.

Q.

The first term of an arithmetic sequence is 5 and the common difference is 2. Find the sum of its first 25 terms.

Q.

Choose the correct alternative to complete the series: $11,32,53,74,95,?$

1. $106$

2. $111$

3. $113$

4. $116$

Q.

Sum of three consecutive terms in an AP is 15 and their product is 0. The sequence is

1. 0, 5, 10.

2. 10, 5, 0.

3. Both a and b

4. None of these.

Q. How to represent 4-square root of 2 in number line

Q. Observe the given pattern and identify what comes next?

1. 
2. 
3. 
4. 

Q.

Question 1 (i)
In which of the following situations does the list of numbers involved make an arithmetic progression and why?
(i) The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

Q. Choose the correct option to complete the arithmetic sequence:
2, 4.5, ___, 9.5, 12, ___, 17

1. 7.5 and 13
2. 6.5 and 13
3. 7 and 14.5
4. 8 and 13.5

Q. 9. Let a and b be natural numbers such that 2a - b, a - 2b, a + b are all distinct squares. What is the smallest possible value of b

Q. Match the patterns with their number patterns.

1. 1, 3, 5
2. 2, 4, 6
3. 1, 4, 7

Q.

Prove that the sum of the first five terms of any arithmetic sequence is five times the middle number. What about the sum of the first seven terms? Can you formulate a general principle from these examples?

Q.

What is arithmetic progression?