problem archive
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A pair of rabbits are too young to produce in their first month. In the second, and every subsequent month, they produce a new pair. Each new pair of ... -
Consider the following lists of numbers: (i) 1, 2, 3, 4, . . . (ii) 100, 70, 40, 10, . . . (iii) -3, -2, -1, 0, . . . (iv) 3, 3, 3, 3, . . . (v) -1.0,... -
For the AP: \( \frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots \), write the first term \(a\) and the common difference \(d\). -
Which of the following list of numbers form an AP? If they form an AP, write the next two terms: (i) 4, 10, 16, 22, \ldots (ii) 1, -1, -3, -5, \ldots ... -
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 ... -
Write first four terms of the AP, when the first term \(a\) and the common difference \(d\) are given as follows: (i) \(a = 10, \ d = 10\) (ii) \(a = ... -
For the following APs, write the first term and the common difference: (i) 3, 1, -1, -3, \ldots (ii) -5, -1, 3, 7, \ldots (iii) \(\frac{1}{3}, \frac{5... -
Which of the following are APs? If they form an AP, find the common difference \(d\) and write three more terms. (i) 2, 4, 8, 16, \ldots (ii) 2, \(\fr... -
Now, looking at the pattern formed above, can you find her monthly salary for the 6th year? The 15th year? And, assuming that she will still be workin... -
Find the 10th term of the AP: 2, 7, 12, ... -
Which term of the AP: 21, 18, 15, ... is -81? Also, is any term 0? Give reason for your answer. -
Determine the AP whose 3rd term is 5 and the 7th term is 9. -
Check whether 301 is a term of the list of numbers 5, 11, 17, 23, \ldots -
In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third, and so on. There are 5 rose plants in the last row. How... -
Fill in the blanks in the following table, given that a is the first term, d the common difference and a_n the nth term of the AP: | a | d | n | a_n... -
Choose the correct choice in the following and justify: (i) 30th term of the AP: 10, 7, 4, ..., is (A) 97 (B) 77 (C) -77 (D) -87 (ii) 11th term of the... -
In the following APs, find the missing terms in the boxes: (i) 2, __, 26 (ii) __, 13, __, 3 (iii) 5, __, 9 1/2 (iv) -4, __, __, __, 6 (v) __, 38, __, ... -
Which term of the AP: 3, 8, 13, 18, ..., is 78? -
Find the number of terms in each of the following APs: (i) 7, 13, 19, ..., 205 (ii) 18, 15 1/2, 13, ..., -47 -
Check whether -150 is a term of the AP: 11, 8, 5, 2, ...