Page 30 - Mathematics Class - X

Viva-Voce

1. Find the sum of first 100 natural numbers using the formula in the activity done above.
Ans. ∑n = n × (n + 1)/2
= 100 (101)/2
= 50 × 101 = 5050

2. If each number in a series of “n” natural numbers is multiplied by 2, what will be the sum of such “n” natural
numbers?
Ans. The sum of the series will be 2∑n or n(n + 1).
3. Find the sum of first 50 even numbers.
Ans. 2 + 4 + 6 + ... + 100
= n(n + 1)

= 50 × 51 = 2550
4. The common difference between two natural numbers is?
Ans. 1

5. Write the general form of any three consecutive even number.
Ans. Any three consecutive even number can be represented as 2n, 2n + 2 and 2n + 4.
6. Can the common difference of an AP be zero?
Ans. Yes.
7. If three terms a, b, c are in AP. Then what is its mandatory condition?

Ans. b – a = c – b
ac+
or 2b = a + c or b =
2

MCQs

1. If the fifth term of an A.P. is 15 and sum of 5 and 6 term is 33, the common difference of A.P is
th
th
a) 2 b) 4 c) 3 d) 8
2. The n term of an A.P is 7 – 4n, find its common difference.
th
a) –5 b) –4 c) 10 d) 6
3. The sum of the first ten natural numbers is

a) 55 b) 54 c) 53 d) 52
4. The sum of the first 15 even numbers is
a) 204 b) 240 c) 150 d) 120
5. The common difference between two consecutive odd numbers is

a) 1 b) –1 c) 2 d) –2

Answers: 1. c) 3 2. b) – 4 3. a) 55 4. b) 240 5. c) 2

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