1Look at pattern (i) with 1, 3 and 5 blocks and pattern (ii) with 2, 4 and 8 blocks. Can you draw two more figures in the same pattern for each?
2Count the blocks and write the number in each figure of the two patterns.
3Observe the numbers of blocks. How are they increasing?
4Can you find the relation that shows how the numbers are increasing?
5Define sequence and series.
6What do you mean by arithmetic sequence?
7Define common difference in an arithmetic sequence.
8Determine with reason whether 3, 7, 11, 15, ... is in arithmetic progression.
9Determine with reason whether 10, 6, 2, -2, ... is in arithmetic progression.
10Determine with reason whether 0, -4, -8, -12, ... is in arithmetic progression.
11Determine with reason whether 5 + 11 + 15 + 23 + ... is in arithmetic progression.
12Determine with reason whether \( -\frac{3}{2}, 2, -\frac{5}{2}, -3, \ldots \) is in arithmetic progression.
13Determine with reason whether \( a, \frac{a+b}{2}, b, \frac{3b-a}{2} \) is in arithmetic progression.
14For the arithmetic sequence -1, -3, -5, -7, ..., find the first term, the common difference, the general term \( t_n \) and the next two terms.
15For the arithmetic sequence 2, 6, 10, 14, ..., find the first term, the common difference, the general term \( t_n \) and the next two terms.
16For the arithmetic sequence 7, 17, 27, 37, ..., find the first term, the common difference, the general term \( t_n \) and the next two terms.
17For the arithmetic sequence \( \frac{5}{4}, 1, \frac{3}{4}, \frac{2}{4}, \ldots \), find the first term, the common difference, the general term \( t_n \) and the next two terms.
18Write the formula for the nth term of an AP.
19Is 7, 12, 17, 22, ... an arithmetic sequence? Write with reasons.
20In \( t_n = a + (n - 1)d \), what does a represent?
21In an arithmetic sequence, the 2nd term is 8 and the common difference is 5. What is the third term?
22In an arithmetic sequence, the tenth term is 120 and the common difference is 8. What is the ninth term?
23In an arithmetic sequence, the 14th term is 150 and the 13th term is 139. Find the common difference.
24In an AP the 6th term is -20 and the 7th term is -25. Find the common difference.
25In an AP, the 2nd and 3rd terms are 10 and 14. Find the 1st term.
26In an arithmetic sequence, the common difference is 7 and the 2nd term is 5. What is the first term?
27The nth term of an AP is \( 6n + 11 \). Find the common difference.
28The nth term of an AP is \( 5n - 2 \). Find the common difference.
29If the first term and the common difference of an AP are 3 and 5, find the 5th term.
30Find the 11th term of an arithmetic sequence whose first term and common difference are 20 and 5.
31Determine the first term of an AP whose common difference is -8 and 10th term is 240.
32What is the first term of an arithmetic sequence whose common difference is 4 and tenth term is 40?
33What is the common difference of an arithmetic sequence whose first term is 150 and 12th term is 40?
34Find the common difference of an arithmetic sequence whose first term and fifth term are 9 and 17.
35Find the number of terms of the AP 7, 13, 19, ..., 205.
36Find the number of terms of the AP \( 18, 15\frac{1}{2}, 13, \ldots, -47 \).
37Find the number of terms of an AP whose first term is 15, common difference is 10 and last term is 115.
38Is 44 a term of the arithmetic sequence 11, 14, 17, ...?
39Does the arithmetic sequence 11, 8, 5, 2, ... contain -150?
40If \( 2x + 3 \), \( x + 11 \) and \( 8x + 3 \) are in AP, find the value of x.
41If \( 8b + 4 \), \( 6b - 2 \) and \( 2b + 7 \) are the first three terms of an AP, find the value of b. Also find the first three terms.
42The 11th and 16th terms of an arithmetic sequence are 38 and 73. Find (i) the first term and common difference, (ii) the 31st term, (iii) the arithmetic sequence.
43The 3rd and 9th terms of an AP are 4 and -8. Find (i) the first term and common difference, (ii) which term of the AP is zero, (iii) whether 10 is a term of the AP, with reason.
44An AP has 47 terms. Its fifth term is 16 and its last term is 100. Find the 20th term.
45An AP has 25 terms. Its 3rd term is 18 and its last term is 128. Find the 15th term.
46In an AP the third term is 16 and the 7th term exceeds the 5th term by 12. Show that the 11th term is 64.
47If 7 times the 7th term of an AP is equal to 11 times its 11th term, show that the 18th term is zero.
48For what value of n are the nth terms of the two APs 63, 65, 67, ... and 3, 10, 17, ... equal?
49If the nth term of the AP 1, 5, 9, 13, ... and the nth term of the AP 43, 46, 49, ... are equal, find the value of n.
50The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
51A man takes a job in 2019 at an annual salary of Rs. 50,000. He receives an annual increase of Rs. 2,000. In which year will his income reach Rs. 70,000?
52After knee surgery, your trainer tells you to return to jogging slowly: 12 minutes a day for the first week, and each week after that, 6 minutes more per day. After how many weeks will you be jogging 60 minutes per day?
53Why is 2, 4, 8, 16, ... a sequence but not an arithmetic sequence?
54Why is it not enough to know only the first term of an AP?
55Find the 12th term of the AP 40, 37, 34, ....