Exams › JEE Advanced › Maths

How many terms are common to both arithmetic sequences: Sequence 1: 17, 21, 25,..., 417 (common difference 4) Sequence 2: 16, 21, 26,..., 466 (common difference 5)?

1. 19
2. 20
3. 21
4. 22

Correct answer: 20

Solution

Both sequences share the term 21. The common terms form an AP with first term 21 and common difference LCM(4,5) = 20: 21, 41, 61,..., up to the largest common term <= 417 (and also <= 466). Largest common term: 21 + 20k <= 417 => 20k <= 396 => k <= 19.8 => k_max = 19. Terms: k = 0, 1, 2,..., 19 => 20 terms.

Related JEE Advanced Maths questions

• If a, b, and c are in harmonic progression, then e raised to the power of -a, e raised to the power of -b, and e raised to the power of -c will be in which progression?
• If x, y, and z represent the pᵗʰ, qᵗʰ, and rᵗʰ terms of both an arithmetic progression and a geometric progression, what is the value of (xʳ)(yᵖ)(zᵠ)?
• Let ϕ(x) represent a quadratic polynomial. Given that ϕ(1) equals ϕ(−1) and the terms a₁, a₂, a₃ form an arithmetic progression, then the values ϕ(a₁), ϕ(a₂), ϕ(a₃) will be in which sequence?
• Let Sₙ = Σ (k+1)/2 * k². Then Sₙ can take value(s)
• If a, b, and c are positive integers such that b is divisible by a, and they form a geometric sequence, while their arithmetic mean equals b + 2, what is the value of (a² + a - 14)/(a + 1)?
• Let bᵢ > 1 for i = 1, 2,..., 101. Assume that logₑb₁, logₑb₂,..., logₑb₁₀₁ form an arithmetic sequence with a common difference of log₂. Also, let a₁, a₂,..., a₁₀₁ form an arithmetic sequence where a₁ = b₁ and a₅₁ = b₅₁. If t represents the sum b₁ + b₂ +... + b₅₁ and s represents the sum a₁ + a₂ +... + a₅₁, then which of the following is true?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →