AP with negative difference: 13, 8, 3, −2, … Find the 10th term.
Aptitude
Odd Man Out and Series
Difficulty: Easy
Choose an option
-
A- 32
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B- 64
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C- 30
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D- 13
Answer
Correct Answer: - 32
Explanation
Introduction / Context:This AP decreases by a constant amount each step. The nth-term formula still applies regardless of sign of the common difference.
Given Data / Assumptions:
- a_1 = 13, d = −5 (since 8−13 = −5).
- Find a_10.
Concept / Approach:Use a_n = a_1 + (n−1)d. Substitute n = 10, a_1 = 13, d = −5.
Step-by-Step Solution:a_10 = 13 + 9*(−5) = 13 − 45 = −32.
Verification / Alternative check:Compute a_5 = −2, then proceed five more steps of −5 each to get −27, −32 (consistent at a_10).
Why Other Options Are Wrong:−64 and −30 are off the correct count of steps; −13 corresponds to a_6, not a_10.
Common Pitfalls:Using n*d instead of (n−1)d, or miscounting negative increments.
Final Answer:- 32