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Published on: 13/05/2022
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Questions + Answers key
Take MCQ Maths Test1.
Find the sum of first 24 terms of the list of numbers whose nth term is given by an = 3 + 2n.
2.
If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.
3.
Determine the AP whose 3rd term is 5 and the 7th term is 9.
4.
Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
-2, 2, -2, 2, -2
5.
Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
4,10,16, 22, ...
1.
an = 3 +2n
a1 = 3 + 2 = 5
a2 = 3 + 2 x 2 = 7
a3 = 3 + 2 x 3 = 9
List of numbers becomes 5, 7, 9, 11,.........
Here, 7 - 5 = 9 - 7 = 11 - 9 = 2 and so on. So, it forms an A.P. with common difference d = 2.
To find S24 we have n = 24, a = 5, d = 2.
S24 = \(\frac{24}{2}\) [2 x 5 + (24 - 1) x ]
= 12 [10 + 46] = 672.
So, sum of first 24 terms of the list of numbers is 672.
2.
Here S14 = 1050
n = 14
a = 10
Sn = \(\frac{n}{2}\) 2(2a + (n -1)d)
1050 = \(\frac{14}{2}\)(20 + 13d)
= 140 + 91d
910 = 91d
d = 10
a20 = 10 + (20 - 1) x 10
= 20
∴ 20th term = 200.
3.
We have
a3 = a + (3 - 1)d = a + 2d = 5 (1)
a7 = a + (7 - 1)d = a + 6d = 9 (2)
(1) - (2) ⇒ -4d -4 ⇒ d = 1.
Sub, d = 1 in (1), we get
a + 2(1) = 5
a = 3
Hence the required A.P. is 3, 4, 5, 6, 7.
4.
-2, 2, -2, 2, -2
t2 - t1 = 2-(-2) = 4
t3 - t2 = -2 -2 = -4
t4 - t3 = 2 - (-2) = 4
It is not an A.P.
5.
4, 10, 16,22, ...
We have a2 - a2 = 10 - 4 = 6
a3 - a2 = 16 -10 = 6
ஃ It is an A.P. with common difference 6
ஃ The next two terms are, 
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Tamilnadu Stateboard 10th Standard Subjects
Tamilnadu Stateboard Standards
