More practice questions

5. Q5. Insert 5 arithmetic means between 8 and 26.

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   d = (26 − 8)/6 = 3: the means are 11, 14, 17, 20, 23.

6. Q6. The sum of the first n terms of an A.P. is 3n² + 5n. Find its 25th term.

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   a₂₅ = S₂₅ − S₂₄ = 3(625 − 576) + 5 = 147 + 5 = 152.

7. Q7. Find the sum of the first 20 odd numbers, and of 1 + 2 + … + 100.

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   1 + 3 + … + 39 = (20/2)(1 + 39) = 400 = 20². 1 + 2 + … + 100 = 100 × 101/2 = 5050.

8. Q8. Which term of the A.P. 21, 18, 15, … is −81?

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   21 + (n − 1)(−3) = −81 gives n − 1 = 34, so −81 is the 35th term.