Question

The first and last terms of a 10-term arithmetic series are listed in the table. What is the sum of the series?

Term Number Term
1 3
10 75

195
390
780
1125

Answer 1

b. 390

Explanation:

`a_1 =3\\a_n=75\\n=10\\\\use \ the \ arithmetic\  formula \\\\S_n=(n)/(2)(a_1+a_n)\\S_1_0=(10)/(2) (3+75)\\\\ \\S_1_0= 5 (78)\\\\S_1_0=390\\`

Answer 2

The arithmetic sequence general formula is an = a1 + d *(n-1) where d is the arithmetic difference and n is an integer. In this case, upon derivation, the formula that represents the sum of the series is S = (a1  + an)*(n/2). Substituting, S = (3+75)*(10/2) equal to 390