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22. The first term of an A.P 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
4 11
(b) 6
(c) 4/11
(d) none of these
مد?
Most Upvoted Answer
22. The first term of an A.P is 14 and the sums of the first five term...
Given Information:
- First term of the AP (Arithmetic Progression) is 14
- Sum of the first five terms and the sum of the first ten terms are equal in magnitude but opposite in sign

Approach:
To find the 3rd term of the AP, we will first find the common difference (d) using the given information that the sums of the first five terms and the first ten terms are equal in magnitude but opposite in sign. Let's denote the common difference as 'd'.

Finding the Common Difference:
Let the common difference be 'd'. The sum of the first five terms of an AP is given by:
S5 = 5/2 [2a + (5-1)d] = 5/2 [2(14) + 4d] = 5(14 + 2d)
Similarly, the sum of the first ten terms of the AP is:
S10 = 10/2 [2a + (10-1)d] = 10/2 [2(14) + 9d] = 5 [28 + 9d]
Given that the sums are equal in magnitude but opposite in sign:
5(14 + 2d) = -5 [28 + 9d]
70 + 10d = -140 - 45d
55d = -210
d = -210/55
d = -42/11

Finding the 3rd Term:
To find the 3rd term of the AP, we use the formula:
a3 = a1 + 2d
a3 = 14 + 2(-42/11)
a3 = 14 - 84/11
a3 = 154/11 - 84/11
a3 = 70/11
Therefore, the 3rd term of the AP is 70/11 or 6.36. Hence, the correct answer is option (b) 6.
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22. The first term of an A.P 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 is4 11(b) 6(c) 4/11(d) none of theseمد?
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22. The first term of an A.P 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 is4 11(b) 6(c) 4/11(d) none of theseمد? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 22. The first term of an A.P 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 is4 11(b) 6(c) 4/11(d) none of theseمد? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 22. The first term of an A.P 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 is4 11(b) 6(c) 4/11(d) none of theseمد?.
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