Arithmetic Progressions Test

Result

Arithmetic Progressions Test - 3

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

If the sum of the first 11 terms of an AP equals the sum of the first 19 terms, then what is the sum of the first 30 terms?

A
0

B
-1

C
1

D
None of these

Solution

S₁₁ = S₁₉

This means that the sum of terms from T₁₂ to T₁₉ is zero; which indicates that out of these 8 terms, half are positive and half are negative with same magnitude. Also, the next 11 terms have the same sum as the first 11 terms are having, but of opposite sign. This will result in the sum of the first 30 terms as 0 (zero).
Question 2
1 / -0

The interior angles of a polygon are in A.P. If the least angle is 42° and common difference is 33°, the number of sides is

A
11

B
10

C
5

D
4

Solution

Given: a = 42°, d = 33°

Sum of all the interior angles of an n-sided polygon is (n - 2)180°.
Therefore, (n - 2)180° = n/2[2a + (n - 1)d]
(n - 2) × 180 = (n/2)(2 × 42 + (n - 1) × 33)

360n - 720 = 84n + 33n² - 33n
11n² - 103n + 240 = 0

(n - 5)(11n - 48) = 0
This implies, n = 5 as sides can't be fraction in number.
Question 3
1 / -0

If the 17^th term of an A.P. is 2 times its 15^th term and the common difference is 6, then what would be the 18^th term of the A.P.?

A
30

B
28

C
25

D
20

Solution

According to question,
The 17^th term of an A.P. is 2 times its 15^th term.

a + 16d = 2(a + 14d)
16d - 28d = 2a - a

-12d = a [Equation 1]
T₁₈ = a + (n - 1)d

= a + (18 - 1)d
= a + 17d

= -12d + 17d [From equation 1]
= 5d = 5(6) = 30