In an arithmetic progression where a_5 = 33 and a_11 = 75, what is a_1?
Answer and explanation
Correct answer: 5
The governing relation is a_n = a_1 + (n - 1)d. Applying it to the two given terms gives a_5 = a_1 + 4d = 33 and a_11 = a_1 + 10d = 75. Subtracting the first equation from the second eliminates a_1: 6d = 42, so d = 7. Substituting into a_1 + 4(7) = 33 gives a_1 + 28 = 33, hence a_1 = 5. Option B is correct. A quick check produces the fifth term 5 + 4×7 = 33 and the eleventh term 5 + 10×7 = 75. The other options fail one or both of these conditions.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The governing relation is a_n = a_1 + (n - 1)d. Applying it to the two given terms gives a_5 = a_1 + 4d = 33 and a_11 = a_1 + 10d = 75. Subtracting the first equation from the second eliminates a_1: 6d = 42, so d = 7. Substituting into a_1 + 4(7) = 33 gives a_1 + 28 = 33, hence a_1 = 5. Option B is correct. A quick check produces the fifth term 5 + 4×7 = 33 and the eleventh term 5 + 10×7 = 75. The other options fail one or both of these conditions.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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