# CBSE 10 Mathematics Arithmetic Progressions Practice Paper 06

1. Write the first term \(a\) and the common difference \(d\) of the following AP’s

(a) \(\frac{3}{ 2}\), \(\frac{1}{ 2}\), \(\frac{-1}{ 2}\), \(\frac{-3}{ 2}\),…..

(b) \(\sqrt{3} , \sqrt{6},\sqrt{9} , \sqrt{12}\), . . .

(c) \(\sqrt{3} , \sqrt{6},\sqrt{9} , \sqrt{12}\), . . .

2. 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 many rows are there in the flower bed?

3. Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

4. If the 3rd and the 9th terms of an AP are 6 and – 6 respectively, which term of this AP is zero?

5. The 15th term of an AP exceeds its 13th term by 6. Find the common difference.

6. How many multiples of 4 lie between 10 and 250?

7. For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

8. Subham Rao started work in 1995 at an annual salary of 5000 and received an increment of 200 each year. In which year did his income reach 7000?

9. Find the sum of the following APs:

(a) 2, 5, 8 . . .to 10 terms. (b) –37, –32, –27, . . .to 12 terms.

(c) 0.5, 1, 1.5, . . .to 100 terms. (d) \(\frac{1}{15}\), \(\frac{1}{12}\), \(\frac{1}{10}\), . . . to 11 terms.

10. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.7 cm, 1.2 cm, 1.7 cm, 2.2 cm, . . . as shown in Fig. 1. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take \(\pi = \frac{22}{7}\))

11. If the sum of the first n terms of an AP is \(4n – n^2\), what is the first term? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

12. Find the sum of the first 39 positive integers divisible by 6.

13. Find the 10th term of the AP : 2, 5, 8, . . .

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