ARITHMETICAL PROGRESSION. 307
EXAMPLES XXXIV. b.
Find the series in which
1. The 27th term is 186, and the 45th term 312. 2. The 5th term is 1, and the 31st term - 77. 3. The 15th term is - 25, and the 23rd term - 41. 4. The 9th term is - 11, and the 102nd term - 150 1/2. 5. The 15th term is 25, and the 29th term 46. 6. The 16th term is 214, and the 51st term 739. 7. The 3rd and 7th terms of an A. P. are 7 and 19 ; find the 15th term. 8. The 54th and 4th terms are — 125 and 0; find the 42nd term. 9. The 31st and 2nd terms are i and 7| ; find the 59th term. 10. Insert 15 arithmetic means between 71 and 23. 11. Insert 17 arithmetic means between 93 and 69. 12. Insert 14 arithmetic means between — 71 and — 21. 13. Insert 16 arithmetic means between 7.2 and - 6.4. 14.
How many terms must be taken of
15. The series 42, 39, -36, ... to make 315 ? 16. The series - 16, - 15, - 14. ... to make - 100 ? 17. The series 15f, 15i, 15, ... to make 129 ? 18. The series 20, 18f, 17 J, ... to make 162^ ? 19. The series - 10^, - 9, - 7i^, ... to make - 42 ? 20. The series - 6|, - 6f , - 6, ... to make - 52i ? 21. The sum of three numbers in A. P. is 39, and their product is 2184 : find them. 22. The sum of three numbers in A. P. is 12, and the sum of their squares is 66 : find them. 23. The sum of five numbers in A. P. is 75, and the product of the greatest and least is 161 : find them. 24. The sum of five numbers in A. P. is 40, and the sum of their squares is 410 : find them. 25. The 12th, 85th, and last terms of an A. P. are 38, 257, 395 respectively: find the number of terms.
