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The first term of an ap is 14 and the sums of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the ap is A)70/11 B)6 C)4/11 D)none?
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The first term of an ap is 14 and the sums of the first five terms and...
Given:

  • First term of AP = 14

  • Sum of first five terms = - Sum of first ten terms


To find: Third term of AP

Solution:
Let the common difference of AP be 'd'.
Then, the second term of AP will be 14 + d and the third term of AP will be 14 + 2d.

The sum of first five terms of the AP can be written as:
S5 = (5/2)[2(14) + (5-1)d]
S5 = 35 + 2d

The sum of first ten terms of the AP can be written as:
S10 = (10/2)[2(14) + (10-1)d]
S10 = 5(14 + 4d)

Given that S5 = -S10
35 + 2d = -5(14 + 4d)
35 + 2d = -70 - 20d
22d = -105
d = -105/22

The third term of the AP can be written as:
14 + 2d = 14 + 2(-105/22)
= 14 - 105/11
= (154 - 105)/11
= 49/11

Therefore, the third term of the AP is 49/11.

Note: The options given in the question are not correct.
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The first term of an ap is 14 and the sums of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the ap is A)70/11 B)6 C)4/11 D)none?
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The first term of an ap is 14 and the sums of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the ap is A)70/11 B)6 C)4/11 D)none? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The first term of an ap is 14 and the sums of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the ap is A)70/11 B)6 C)4/11 D)none? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first term of an ap is 14 and the sums of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the ap is A)70/11 B)6 C)4/11 D)none?.
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