...are 3 and 25, and the number of terms is 12 : what is the sum of all the terms? An*. 168. 2. What is the sum of the natural series of numbers, 1, 2, 3, 4, 5, &c., up to 100? 3. How many strokes does a common clock strike in 12 hours? GO 4. To find the common...

...purchase ? NOTE. Questions similar to the Jour preceding ones may be performed by Alligation. 141. What is the sum of the natural series of "numbers 1, 2, 3, 4, 5, &c., up to 10000? 142. A man rents his store for $500 a year, the rent to be paid at the end of...

...is called its present worth. PROBLEM I. To find the amount of an annuity at simple interest. RULE.* Find the sum of the natural series of numbers, 1, 2, 3, &c. to the number of years less one. Then multiply this sum by one year's interest of the annuity,...

...progression, 1, 9, 17, &c., the new series will be 1, 3, 5, 7, 9, 11, 13, 15, 17, and so on. EXAMPLES. 1. Find the sum of the natural series of numbers 1,...term, and the sum of the series of odd numbers 1, 3, 5, 7, . . . continued to 101 terms. Ans. 201 and 10201 3. How many times does a common clock strike,...

...square of the number of terms. Thus, 1+3 = 4=2'. 1+3+5 = 9=3'. 1+3 + 5+7 =16=4'. 1+3+5+7+9=25=5'. Ex. 9. Find the sum of the natural series of numbers 1, 2, 3, 4, 5, &c., up to M terms. «(n+l) *' 2 " Ex. 10. Find the sum of the even numbers 2, 4, 6, 8, &c., up...

...difference is 5, the number of terms 6, and the sum 321. Ans. The first term = 41, the last term = 66. 22. Find the sum of the natural series of numbers 1, 2, 3, &c. up to n terms. Ans. % n (n--j- 1). 23. Find the sum of the natural series of numbers from 1 to...

...terms, when the first term, the last term and the number of the terms are given. EXAMPLES. 1. What is the sum of the natural series of numbers 1, 2, 3, 4, &c. up to 1000 ? 3. What is the sum of the uneven numbers 1, 3, 5, 7, &c. up to 93 ? 171. The equations...

...is equal to the sum of any other two terms equally distant from the extremes. Examples. 1. What is the sum of the natural series of numbers 1, 2, 3, 4, 5, etc., up to 25 ? Ans. S= 2. The extremes of an arithmetical progression are 2 and 50, and the number...

...added to the sum of the 4 instalments, viz., $400, gives $436, as in the 1st method. Hence, RULE. — Find the sum of the natural series of numbers, 1, 2, 3, etc., up to the number of instalments, less one, by Art. 351 ; multiply the interest of one instalment...

...terms, when the first term, the last term and the number of the terms are given. EXAMPLES. 1. What is the sum of the natural series of numbers 1, 2, 3, 4, &c. up to 1000 ? 3. What is the sum of the uneven numbers 1, 3, 5, 7, &c, up to 93 ? 171. The equations...