Skip to content 1 Can the same approach (refer to NCERT page no.
SA (Short)
2 Observe the Sierpiński triangle.
LA (Long)
3 Can you use this formula to find S20, S50 or S1000?
SA (Short)
4 Let us revisit the sequence tn of triangular numbers 1, 3, 6, 10, 15, shown in the given figure.
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5 Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
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6 Can you predict the number of squares in Stages 5 and 6 of the pattern (3, 6, 12, 24)?
LA (Long)
7 How many three-digit numbers are divisible by 7?
SA (Short)
8 How many multiples of 4 lie between 10 and 250?
SA (Short)
9 Find all possible ways of expressing 100 as the sum of consecutive natural numbers.
LA (Long)
10 Determine the AP whose third term is 16 and whose 7th term exceeds the 5th term by 12.
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11 Find a GP for which the sum of the first two terms is -4 and the fifth term is 4 times the third term.
LA (Long)
12 The sum of the 4th and 8th terms of an AP is 24, and the sum of the 6th and 10th terms is 44.
LA (Long)
13 Find the smallest value of n such that the sum of the first n natural numbers is greater than 1,000.
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14 Which term of the G.P.: 2, 8, 32, is 131072? Write the explicit formula as well as the recursive formula for the nth term.
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15 The sum of the first three terms of a GP is 13/12 and their product is -1.
LA (Long)
16 The number of bacteria in a certain culture doubles every hour.
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17 The sum of the first three terms of a geometric progression is 26, and the sum of their squares is 364.
LA (Long)
18 Suppose P1 = 1, P2 = 2, and for n > 2, Pn = P1 + P2 + + Pn-1 + 1.Find the values of P1, P2, , P8. Can you find a simpler recursive formula for Pn?Can you give an explicit formula?
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19 Suppose W1 = 1, W2 = 2 and for n > 2, Wn = W1 + W2 + + Wn-2 + 2.Find the values of W1, W2, , W8. Do you recognise this sequence?
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20 If the 4th, 10th, and 16th terms of a GP are x, y, and z respectively, prove that x, y, z are in GP.
LA (Long)
21 Find the 10th and 26th terms of the A.P.: 3, 8, 13, 18, [Page No. 185]
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22 Which term of the AP: 21, 18, 15, ... is -81? Also, is 0 a term of this AP? Give reasons for your answer. [Page No. 185]
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23 Find the nth term of the A.P.: 11,8,5,2,... . Write the recursive rule for this A.P. [Page No. 185]
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24 How many 2-digit numbers are divisible by 3?
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25 Harish started work at an annual salary of ₹ 5,00,000 and received an increment of ₹ 20,000 each year.
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26 An A.P. consists of 50 terms in which the 3rd term is 12 and the last term is 106. Find the 29th term. (Hint: If a is the first term and d the common difference, then we arrive at…
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27 A child arranges marbles in rows so that the first row has 1 marble, the second has 2 marbles, the third has 3, and so on up to 25 rows.
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28 Find the 12th term of a G.P. with common ratio 2, whose 8th term is 192. [Page No. 193]
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29 Which term of the G.P.: 2, 6, 18, ... is 4374? Write the explicit formula as well as the recursive formula for the nth term. [Page No. 193]
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30 A sequence is given by the recursive rule t1 = 2, tn+1 = 3tn - 2 for n ≥ 1.
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