Arithmetic Progression worksheet-1
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1. In the Arithmetic process, if a = 28, d = -4, n = 7, then:
(a) 4
(b) 5
(c) 3
(d) 7
Answer: a
Description: By AP,
a = a + (n-1) d
= 28+ (7-1) (- 4)
= 28 + 6 (-4)
= 28-24
i = 4
2. If = 10 and d = 10, the first four goals will be:
(a) 10,30,50,60
(b) 10,20,30,40
(c) 10,15,20,25
(d) 10,18,20,30
Answer: b
Definition: a = 10, d = 10
a1 = a = 10
a2 = a1 + d = 10 + 10 = 20
a3 = a2 + d = 20 + 10 = 30
a4 = a3 + d = 30 + 10 = 40
3.The first sentence and the standard variation of A.P. 3,1, -1, -3 states:
(a) 1 and 3
(b) -1 and 3
(c) 3 and 2
(d) 2 and 3
Answer: c
Definition: First term, a = 3
Standard difference, d = Second term - First term
⇒ 1 - 3 = 2
⇒ d = 2
4.30th Time A.P: 10.7, 4,…,
(a) 97
(b) 77
(c) -77
(d) -87
Answer: c
Definition: Given,
A.P. = 10, 7, 4,…
First term, a = 10
Normal difference, d = a2 - a1 = 7−10 = −3
As we know, by A.P.
i = a + (n - 1) d
Pricing;
a30 = 10+ (30−1) (- 3)
a30 = 10+ (29) (- 3)
a30 = 10−87 = −77
5.11 time of A.P. -3, -1 / 2 ,, 2…. Is
(a) 28
(b) 22
(c) -38
(d) -48
Answer: b
Description: A.P. = -3, -1 / 2 ,, 2…
First term a = - 3
Standard difference, d = a2 - a1 = (-1 / 2) - (- 3)
⇒ (-1 / 2) + 3 = 5/2
Nth term;
i = a + (n - 1) d
Pricing;
a11 = 3+ (11-1) (5/2)
a11 = 3+ (10) (5/2)
a11 = -3 + 25
a11 = 22
6. The missing word in the AP: __, 13, __, 3 is:
(a) 11 and 9
(b) 17 and 9
(c) 18 and 8
(d) 18 and 9
Answer: (c)
Definition: a2 = 13 no
a4 = 3
Nth time for AP;
i = a + (n - 1) d
a2 = a + (2-1) d
13 = a + d ………………………. (i)
a4 = a + (4-1) d
3 = a + 3d ………… .. (ii)
Subtracting equation (i) from (ii), we find,
- 10 = 2d
d = - 5
Now enter the value of d in 1
13 = a + (- 5)
a = 18 (first name)
a3 = 18+ (3-1) (- 5)
= 18 + 2 (-5) = 18-10 = 8 (third term).
7.How long for A.P. 3, 8, 13, 18,… is 78?
(a) 12
(b) 13
(c) 15
(d) 16
Answer: (d)
Description: Given, 3, 8, 13, 18,… by AP.
First term, a = 3
Normal difference, d = a2 - a1 = 8 - 3 = 5
Enable nth name for A.P. given 78. Now as we know,
i = a + (n - 1) d
Therefore,
78 = 3+ (n −1) 5
75 = (n - 1) 5
(n - 1) = 15
n = 16
8. The 21st name of the AP is its first 3 and 4 names are:
(a) 17
(b) 137
(c) 143
(d) -143
Answer: b
Definition: First term = -3 and second term = 4
a = -3
d = 4-a = 4 - (- 3) = 7
a21 = a + (21-1) d
= -3 + (20) 7
= -3 + 140
= 137
9. If the 17th period of A.P. exceeds its 10th time by 7. The most common difference is:
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (a)
Definition: Nth time in AP by:
a = a + (n-1) d
a17 = a + (17−1) d
a17 = a + 16d
Vice versa,
a10 = a + 9d
Given,
a17 - a10 = 7
Therefore,
(a + 168d) - (a + 9d) = 7
7d = 7
d = 1
Therefore, the common difference is 1.
10. The number of 4 times between 10 and 250 is:
(a) 50
(b) 40
(c) 60
(d) 30
Answer: (c)
Definition: 4 repetitions after 10 are:
12, 16, 20, 24,…
So here, a = 12 and d = 4
Now, 250/4 gives the remaining 2. So, 250 - 2 - 248 is from 2.
12, 16, 20, 24,…, 248
Therefore, the term nth, i = 248
As we know,
i = a + (n - 1) d
248 = 12+ (n-1) × 4
236/4 = n-1
59 = n-1
n = 60
11. Term 20 is from the last term of A.P. 3, 8, 13,…, 253 are:
(a) 147
(b) 151
(c) 154
(d) 158
Answer: (d)
Description: Given, A.P. by 3, 8, 13,…, 253
Standard difference, d = 5.
By postponing,
253, 248, 243,…, 13, 8, 5
Therefore,
a = 253
d = 248 - 253 = −5
n = 20
With nth formula,
a20 = a + (20−1) d
a20 = 253+ (19) (- 5)
a20 = 253−95
a20 = 158
12. The total of the first five dimensions of 3 is:
(a) 45
(b) 55
(c) 65
(d) 75
Answer: (a)
Definition: The first five duplicates are 3,6,9,12 and 15
a = 3 no d = 3
n = 5
ISum, Sn = n / 2 [2a + (n-1) d]
S5 = 5/2 [2.3+ (5-1) 3]
= 5/2 [6 + 12]
= 5/2 [18]
= 5 x 9
= 45
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