Page:Elementary algebra (1896).djvu/442

424 Rh Find the number of shot in :

3. A square pile, having 15 shot in each side of the base. 4. A triangular pile, having 18 shot in each side of the base. 5. A rectangular pile, the length and the breadth of the base containing 50 and 28 shot respectively. 6. An incomplete triangular pile, a side of the base having 25 shot, and a side of the top 14. 7. An incomplete square pile of 27 courses, having 40 shot in each side of the base. 8. Find the ninth term and the sum of the first nine terms of the series 1, 3 + 5, 7 + 9 + 11, $$\ldots$$.

The numbers 1, 2, 3, $$\ldots$$. are often referred to as the natural numbers.

9. Find the sum of the squares of the first n natural numbers. 10. Find the sum of the cubes of the first n natural numbers. 11. The number of shot in a complete rectangular pile is 24395 ; if there are 34 shot in the breadth of the base, how many are there in its length ? 12. The number of shot in the top layer of a square pile is 169, and in the lowest layer is 1089 ; how many shot does the pile contain ? 13. Find the number of shot in a complete rectangular pile of 15 courses, having 20 shot in the longer side of its base. 14. Find the number of shot in an incomplete rectangular pile, the number of shot in the sides of its upper course being 11 and 18, and the number in the shorter side of its lowest course being 30.

Find the nth. term and the sum of n terms of the series :

15. 4, 14, 30, 52, 80, 114, $$\ldots$$. 16. 8, 26, 54, 92, 140, 198, $$\ldots$$. 17. 2, 12, 36, 80, 150, 252, $$\ldots$$. 18. 8, 16, 0, -64, -200, -432,$$\ldots$$. 19. 30, 144, 420, 960, 1890, 3360, $$\ldots$$.

20. What is the number of shot required to complete a rectangular pile having 15 and 6 shot in the longer and shorter side, respectively, of its upper course ? 21. The number of shot in a triangular pile is greater by 150 than half the number of shot in a square pile, the number of layers in each being the same : find the number of shot in the lowest layer of the triangular pile.