If a₈ = 44 and d = −2, what is the 12th term?
Answer and explanation
Correct answer: 36
The governing concept is the nth-term relation for an arithmetic progression, including a negative common difference: aₙ = aᵣ + (n − r)d. The twelfth term is 12 − 8 = 4 steps after the eighth term. Hence a₁₂ = 44 + 4(−2) = 44 − 8 = 36, so option B is correct. The negative sign means the sequence decreases by 2 at every step; the relevant terms are 44, 42, 40, 38, and 36. Option A would subtract five differences, option C would subtract only three, and option D would subtract only two. Keeping the negative sign throughout the substitution is important, because changing it to positive would incorrectly make the sequence increase rather than decrease.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
The governing concept is the nth-term relation for an arithmetic progression, including a negative common difference: aₙ = aᵣ + (n − r)d. The twelfth term is 12 − 8 = 4 steps after the eighth term. Hence a₁₂ = 44 + 4(−2) = 44 − 8 = 36, so option B is correct. The negative sign means the sequence decreases by 2 at every step; the relevant terms are 44, 42, 40, 38, and 36. Option A would subtract five differences, option C would subtract only three, and option D would subtract only two. Keeping the negative sign throughout the substitution is important, because changing it to positive would incorrectly make the sequence increase rather than decrease.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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