In an arithmetic progression, a₃ = 15 and a₇ = 35. What is a₁?
Answer and explanation
Correct answer: 5
Use the arithmetic-progression rule aₙ = a₁ + (n − 1)d. From a₃ = a₁ + 2d = 15 and a₇ = a₁ + 6d = 35, subtract the first equation from the second: 4d = 20, so d = 5. Substituting this into a₁ + 2d = 15 gives a₁ + 10 = 15, hence a₁ = 5. Another way is to note that four equal steps carry the sequence from the third to the seventh term, so each step increases by 20/4 = 5. Options A, C, and D would not produce both given terms with the same common difference. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Use the arithmetic-progression rule aₙ = a₁ + (n − 1)d. From a₃ = a₁ + 2d = 15 and a₇ = a₁ + 6d = 35, subtract the first equation from the second: 4d = 20, so d = 5. Substituting this into a₁ + 2d = 15 gives a₁ + 10 = 15, hence a₁ = 5. Another way is to note that four equal steps carry the sequence from the third to the seventh term, so each step increases by 20/4 = 5. Options A, C, and D would not produce both given terms with the same common difference. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
