Terms in a Sequence

Q. The general term of a sequence is give by a_n = −4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.

Q.

The sum of interior angles of an equilateral triangle, a regular quadrilateral, a regular pentagon.....etc written as a sequence is

1. ${90}^{\circ },{360}^{\circ },{540}^{\circ }\cdots \cdots$

2. ${360}^{\circ },{540}^{\circ },{720}^{\circ }\cdots \cdots$

3. ${90}^{\circ },{180}^{\circ },{360}^{\circ }\cdots \cdots$

4. ${180}^{\circ },{360}^{\circ },{540}^{\circ }\cdots \cdots$

Q. Show that the sequence defined by a_n = 3n² − 5 is not an A.P.

Q.

Two numbers are successively drawn from the set $U=\left\{1,2,3,4,5,6,7,8\right\}$ the second being drawn without replacing the first. The number of elementary events in the sample is:

1. $64$

2. $56$

3. $32$

4. $14$

Q. If the numbers 2n − 1, 3n + 2 and 6n − 1 are in AP, then find n and hence find the numbers.

Q. Consider the AP: 5, 7, 9, 11, 13...
If each term of the given AP is multiplied by 3, the common difference of the new AP formed will be

1. 2
2. 6
3. 8
4. 5

Q.

Which of the following sequence are in A.P. ?

(a) 3, 7, 11, 15, …….

(b) 8, 4, 2, 1, ……..

(c) 1, −1, −3, −5, …….

Q. Find the common difference of an AP in which a18-a14=32

Q. The list of numbers 5, - 2, -9, -16 ...is an AP with d = 7.

1. An AP with d = -7
2. An AP with d = 7

Q. Pick the incorrect statement from the below options based on the folllowing information:
The list of numbers 5, - 2, -9, -16 ...

1. An AP with d = -7
2. An AP with d = 7
3. An AP with d = 3
4. Not an AP

Q. If $T_n=78$, where $T_n$ denotes the $n^{th}$ term the following A.P.:
$3,8,13,18$, . . . , then find the value of $n$.
[3 Marks]

Q. Show that the sequence defined by a_n = 5n −7 is an A.P, find its common difference.

Q. Difference between ap and gp

Q. Find the sum of all the natural numbers between 100 and 1000 which are multiples of 7?

Q.

Which of the following sequence are in A.P. ?

(a) 3, 7, 11, 15, …….

(b) 8, 4, 2, 1, ……..

(c) 1, −1, −3, −5, …….

Q.

See the figures made with matchsticks:

The numbers of sticks needed for the next figure is

1. 18

2. 16

3. 19

4. 15

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. If 8 times the 8th term of an APis equal to 15 times of 15th term find its 23rd term

Q. Find sum of multiples of 9 between 300 and 700

Q. 8 terms are inserted between 5 and 43 so that the resulting sequence is an AP. The sum of the resulting AP is.

1. 240
2. 440
3. 260
4. 280