Progressions. i 09 



J. The first term is 8^, the common difference — f, and the 

 number of terms 29 ; what is the sum ? 



4. The first term is f, the common difference f, and the 

 number of terms 1 2 ; what is the sum ? 



5. Insert 10 arithmetical maeans between —J and -fj. 



6. Find the sum of the first ;/ odd numbers i +3 + 5-I-7, etc. 



7. Find the sum of ?^ terms of the progression of natural 

 numbers 1 + 2 + 3 + 4, ^te- 

 cs'. Find the sum of ?i terms of the progression of even 



numbers + 2 + 4 + 6 + 8, etc. 



p. The first term is 11, the common difference —2, ^nd the 

 sum 27. Find the number of terms. 



10. The first term is 4, the common difference is 2, and the 

 sum 18. Find the number of terms. 



11. The first term is 11, the common difference is —3, and 

 the sum 24. Find the number of terms. 



12. The sum of ?i consecutive odd numbers is s. Find the 

 first of the numbers. 



ij. Select 10 consecutive numbers from the natural scale 

 whose sum shall be 1000. 



14. Sum \/i-+ V2 + 3Vi+ etc., to twenty terms. 



75. Sum 5 — 2 — 9—16— etc., to eight terms. 



16. Find the tenth term of the arithmetical progression 

 whose first and sixteenth terms are 2 and 48 ; and also detenn- 

 ine the sum of those eight terms the last of which is 60. 



ly. Insert five arithmetical means between 10 and 8. 



18. Insert four arithmetical means between —2 and —16. 



19. How many terms must be taken from the commence- 

 ment of the series 1 + 5 + 9+13+17 etc. , so that the sum of the 1 3 

 succeeding terms may be 741 ? 



20. Wnat is the expression for the sum of ;/ terms of an 

 arithmetical progression whose first term is | and the difference 

 of whose third and seventh terms is 3 ? 



21. The sum of the first three terms of an arithmetical pro- 



