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July 27, 2023
Here, are quick and easy Tips and Tricks for AP and GP and HP for you to help in AP, GP, and HP questions quickly, easily, and efficiently in competitive exams.
There are many Applications of AP and GP and HP as well as they are Very Important Topics from Examination Point of View.
Here, are some easy tips and tricks for you to solve AP, GP and HP questions quickly, easily, and efficiently in competitive exams.
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Find 10th term in the series 2, 5, 8, 11, 14……
Options:
We know that,
tn = a + (n – 1)dIn the given series,
a = 2d = 3 …. (5 – 2, 8 – 5…..)
Therefore, 10th term = t10 = a + (n-1) d
t10 = 2 + (10 – 1) 3
t10 = 2 + 9 x 3
t10 = 29
Correct option: 2
The sum of 3 numbers in arithmetic progression is 36 and product of their extreme is 80. Find the numbers.
Solution:
tn = a + (n – 1)d
Assume the numbers as:
a-d, a, a+d
or a-d+a+a+d=36
or 3a=36
a=12
now (a-d) (a+d)=80
a²-d²=80
144-d²=80
d²=64
d=8
thus the numbers will be: 4, 12 and 20
Find the number of terms in the series 5, 10, 20, . . ..320?
an= arn-1
a = 5r = 2
an= 320320 = 5 x 2n-1
64 = 2n-1
2^{6} = 2n-1
n-1 = 6
n = 7
Correct Option. 4
The sum of three numbers is 14 and their product is 64. All the three numbers are in GP. Find all the three numbers when value of r is a whole number?
1. 3, 6, 4
2. 2, 4, 8
3. 2, 4, 6
4. 4, 4, 4
Solution: The three numbers can be written as (\frac{a}{r}), a, ar
Sum of the three numbers = (\frac{a}{r}) + a + ar = 14
Product of the three numbers = (\frac{a}{r}) \times a \times ar = 64
i.e. a3 =64
Therefore, a = 4
Put the value of a in \frac{a}{r} + a + ar = 14
2(1 + r + r2) = 7r
2r2 – 5r + 2 = 0
r = 2 or \frac{1}{2}
If r = 2, then numbers are 2, 4, 8.If r = \frac{1}{2} then numbers are 8, 4, 2
Correct Option. 2
Find the 15th term in the series \frac{1}{3}, \frac{1}{6}, \frac{1}{9}, \frac{1}{12}…….
Convert the HP series in AP
We get 3, 6, 9, 12……In the given series,
a = 3
d = 3…..(6 – 3)
Therefore, 15th term = a_{15}= a + (n-1) d
a_{15}= 3 + (15– 1) 3
a_{15} = 3 + 14 x 3
a_{15} = 3 + 42
a_{15} = 45
HP a_{15}= \frac{1}{45}
Correct option: 3
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