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XII (12) HSC

XI (11) FYJC
X (10) SSC

### ARITHMETIC PROGRESSION

EX. NO. 1.1

1. For each of the sequence, find the next four terms.

2. Find the first five terms of the following sequences, whose nth terms are given.

3. Find the first three terms of the sequences for which Sn is given below:

(ii)  Sn = [n2(n+1)2]/4  (2 marks)

(iii)  Sn = [n(n+1)(2n+1)]/6  (2 marks)

EXERCISE - 1.2

1. Which of the following lists of numbers are Arithmetic Progressions? Justify.

(iv) 3, 6, 12, 24, .... (1 mark)

(vii) 4, 3, 2, 1, .... (1 mark)

2. Write the first five terms of the following Arithmetic Progressions where, the common difference ‘d’ and the first term ‘a’ are given :

EXERCISE - 1.3

EXERCISE - 1.4

Ex. No. 1.5

Ex. No. 1.6

1. Mary got a job with a starting salary of Rs. 15000/- per month. She will get an incentive of Rs. 100/- per month. What will be her salary after 20 months? [Ans.]

2. The taxi fare is Rs. 14 for the first kilometer and Rs. 2 for each additional kilometer. What will be fare for 10 kilometers ? [Ans.]

3. Mangala started doing physical exercise 10 minutes for the first day. She will increase the time of exercise by 5 minutes per day, till she reaches 45 minutes. How many days are required to reach 45 minutes? [Ans.]

4. There is an auditorium with 35 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row, and so on. Find the number of seats in the twenty fifth row. [Ans.]

5. A village has 4000 literate people in the year 2010 and this number increases by 400 per year. How many literate people will be there till the year 2020 ? Find a formula to know the number of literate people after n years ? [Ans.]

6. Neela saves in a ‘Mahila Bachat gat’ Rs. 2 on the first day, Rs.4 on the second day, Rs. 6 on the third day and so on. What will be her saving in the month of February 2010 ? [Ans.]

7. Babubhai borrows Rs. 4000 and agrees to repay with a total interest of Rs. 500. in 10 instalments, each instalment being less that the preceding instalment by Rs. 10. What should be the first and the last instalment? [Ans.]

8. A meeting hall has 20 seats in the first row, 24 seats in the second row, 28 seats in the third row, and so on and has in all 30 rows. How many seats are there in the meeting hall ? [Ans.]

9. Vijay invests some amount in National saving certificate. For the 1st year he invests Rs. 500, for the 2nd year he invests Rs. 700, for the 3rd year he invests Rs. 900, and so on. How much amount he has invested in 12 years ? [Ans.]

10. In a school, a plantation program was arranged on the occasion of world environment day, on a ground of triangular shape. The trees are to be planted as shown in the figure. One plant in the first row, two in the second row, three in the third row and so on. If there are 25 rows then find the total number of plants to be planted. [Ans.]

Problme Set 1

1. Find t11 from the following A.P. 4, 9, 14, ....  [Ans.]

2. Find the first negative term from the following A.P. 122, 116, 110, .... [Note : Find smallest nth such that tn < 0] [Ans.]

3. Find the sum of first 11 positive numbers which are multiples of 6. [Ans.]

4. In the A.P. 7, 14, 21, ..... how many terms have to be considered for getting sum 5740. [Ans.]

5. From an A.P. first and last terms are 13 and 216. Common difference is 7. How many terms are there in that A.P. Find the sum of all terms. [Ans.]

6. Second and fourth terms of an A.P. is 12 and 20 respectively. Find the sum of first 25 terms of that A.P. [Ans.]

7. If the sum of first n term sof an A.P. is 3n + n2, then find  [Ans.]
(i) first tem and the sum of first two terms.
(ii) 2nd , 3rd, and 15 th terms

8. For an A.P. givne below, find t20 and S10. 1/6, 1/4, 1/3,..... [Ans.]

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