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Published on: 13/05/2022
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Questions + Answers key
Take MCQ Maths Test1.
How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?
2.
In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 is the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?
3.
Which of the following list of numbers form an AP ? If they form an AP, write the next two terms:
1, 1, 1, 2, 2, 2, 3, 3, 3
4.
Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
1,-1,-3, -5, ...
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.
Here a = 24, d = 21-24 = -3, Sn = 78. We need to find n.
We know that,
Sn= \(\frac{n}{2}\) (2a + (n - 1)d)
78 = \(\frac{n}{2}\) 48 + (n -1)(-3))
78 = \(\frac{n}{2}\) 2(51-3n)
or 3n2 - 51n + 156 = 0
n2 -17n + 52 = 0
(n - 4)(n - 13) = 0
n = 4 or 13
The number of terms are 4 or 13.
2.
The number of rose plants in the 1st, 2nd, 3rd, . . . rows are
23,21, 19, ... 5
It forms an A.P.
Let the number of rows in the flower bed be n.
Then a = 23, d = 21 - 23 = -2/a = 5.
As, an = a + (n - 1)d i.e. tn = a + (n - 1)d
We have 5 = 23 + (n - 1)(-2)
i.e. -18 = (n - 1)(-2)
n = 10
ஃ There are 10 rows in the flower bed.
3.
1,1,1,2,2,2,3,3,3
t2 - t1 = 1-1 = 0
t3 - t2 = 1-1 = 0
t4 - t3 = 2-1 = 1
Here t2 - t1 ≠ t3 - t2
ஃ It is not an A.P.
4.
1,-1,-3, -5, ...
t2 - t1 = -1 - 1 = -2
t3 - t2 = -3 - (-1)= -2
t4 - t3 = -5 - (-3) = -2
The given list of numbers form an A.P with the common difference -2.
The next two terms are (-5 + (-2)) = -7, -7 + (-2) = -9.
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
