Patterns, Sequences

Q. Question 2
In an AP, if a = 3.5, d = 0 and n = 101, then $a_n$ will be:

A) 0
B) 3.5
C) 103.5
D) 104.5

Q. Question 4
How many terms of the AP 9, 17, 25 … must be taken to give a sum of 636?

Q.

The missing terms in the arithmetic sequence __, __, 5, 8, 11, __, __, 20 are

1. -1, 4, 15, 18

2. -1, 3, 12, 16

3. 1, 3, 13, 15

4. -1, 2, 14, 17

Q. Question 1 (i)
Which of the following form an AP? Justify your answer.
–1, –1, –1, –1, ……

Q. A person boarded a taxi that charges Rs 15 for the first km and Rs 8 for each additional km. He needs to pay Rs___ if he has to travel 16 km.

Q. In an AP, if the common difference (d) = -4 and the seventh term $\left(a_7\right)$ is 4, then find the first term.

Q. Question 6
The ${21}^{st}$ term of an AP whose first two terms are – 3 and 4, is

A) 17
B) 137
C) 143
D) -143

Q. For the following APs, write the first term and the common difference:
(i) $3,1,-1,-3,....$
(ii) $-5,-1,3,7,.....$
(iii) $\frac{1}{3},\frac{5}{3},\frac{9}{3},\frac{13}{3},....$
(iv) $0.6,1.7,2.8,3.9,...$

Q. Question 27
Find the sum of first 17 terms of an AP whose $4^{th}$ and $9^{th}$ terms are – 15 and –30, respectively.

Q. Find the missing terms in the arithmetic sequence __, __, 5, 8, 11, __, __, 20.

Q. Question 7
The sum of the $5^{th}$ and the $7^{th}$ terms of an AP is 52and the ${10}^{th}$ term is 46. Find the AP.

Q. 18 terms are inserted between 3 and 45 such that the resulting sequence is an AP. The sum of the resulting (finite) AP including the terms 3 and 45 is ___.

Q. Question 4
Two AP’s have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their ${10}^{th}$ terms is the same as the difference between their ${21}^{st}$ terms, which is the same as the difference between any two corresponding terms?Why?

Q.

A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... The total length of such a spiral made up of thirteen consecutive semicircles is ___ ( Round off to the nearest 10)

Q. The sequence of numbers 5, - 2, -9, -16, ...is

1. not an AP.
2. an AP with common difference -7.
3. an AP with common difference 7.
4. an AP with common difference 3.

Q. Question 6
The taxi fare after each km, when the fare is ₹ 15 for the first km and ₹ 8 for each additional km, does not form an AP as the total fare (in ₹) after each km is 15, 8, 8, 8, … Is the statement true? Give reasons.

Q. Check whether – 150 is a term of the AP :11, 8, 5, 2…. ?

Q.

If $x+1,3x$ and $4x+2$ are the first three terms of an AP, then its $5^{\text{th}}$ term is ___.

1. 14

2. 19

3. 24

4. 28

Q.

In an AP, where the first term is 7 and the common difference is 4, ___ ${}^{th}$ term of the AP will be five times the first term. (Enter a number)

Q. A taxi charges ₹15 for the first km and ₹8 for each additional km. The amount payable for 16 km is .

1. ₹125
2. ₹135
3. ₹145

Q.
Which of the following options represents the above figure?

1. Prime numbers
2. Odd numbers
3. Even numbers
4. Square numbers

Q. In an AP, where the first term is 7 and the common difference is 4, ___term of the AP will be five times the first term. (Enter a number)

Q. Question 8
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Q. In an AP, where the first term is 7 and the common difference is 4, ___term of the AP will be five times the first term. (Enter number only)

Q. A person boarded a taxi that charges Rs 15 for the first km and Rs 8 for each additional km. He needs to pay Rs___ if he has to travel 16 km.

Q. Question 5
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Q.

A player who was playing video game was given 20 coins to begin with the game. To go to the next level, he needs to spend 4 coins and if he succeeds the particular level, he earns 6 coins. Find the number of coins he collects after clearing each level (assuming he clears every level).

1. 20, 22, 24, 26, 28………

2. 20, 25, 30, 35, 36………

3. 20, 24, 28, 30, 34………

4. 20, 26, 32, 38, 44………

Q. A taxi charges ₹15 for the first km and ₹8 for each additional km. The amount payable for 16 km is .

1. ₹125
2. ₹135
3. ₹145

Q.

How many two-digit numbers are divisible by $6$?

Q.

Which of the following sequences are APs?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11……..

(iii) -1, -1.25, -1.5, -1.75…….

(iv) 1, -1, -3, -5, -7…………

1. (i), (iii) and (iv)

2. (i) and (iv)

3. (ii) and (iv)

4. (iii) and (iv)