More practice questions

5. Q5. Write the first five terms of (i) a_n = n/(n + 1); (ii) a_n = 2ⁿ (NCERT Exercise 8.1, Q2 and Q3).

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   (i) 1/2, 2/3, 3/4, 4/5, 5/6. (ii) 2, 4, 8, 16, 32.

6. Q6. Write the first five terms of (i) a_n = (2n − 3)/6; (ii) a_n = n(n² + 5)/4 (NCERT Exercise 8.1, Q4 and Q6).

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   (i) −1/6, 1/6, 1/2, 5/6, 7/6. (ii) 3/2, 9/2, 21/2, 21, 75/2; for example a₄ = 4 × 21/4 = 21.

7. Q7. Find (i) a₇ for a_n = n²/2ⁿ; (ii) a₉ for a_n = (−1)ⁿ⁻¹n³ (NCERT Exercise 8.1, Q8 and Q9).

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   (i) a₇ = 7²/2⁷ = 49/128. (ii) 9 is odd, so the sign is +: a₉ = 729.

8. Q8. The Fibonacci sequence is defined by 1 = a₁ = a₂ and a_n = a_n−1 + a_n−2 for n > 2. Find a_n+1/a_n for n = 1, 2, 3, 4, 5 (NCERT Exercise 8.1, Q14).

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   The terms are 1, 1, 2, 3, 5, 8, so the ratios are 1/1 = 1, 2/1 = 2, 3/2, 5/3 and 8/5.