MATH SOLVE

4 months ago

Q:
# A sequence consists of the positive odd integers. What is the sum of the first 12 terms of the sequence? A. 144 B. 169 C. 115 D. 121

Accepted Solution

A:

Answer:AStep-by-step explanation:The sequence of positive odd numbers is1, 3, 5, 7, ......This is an arithmetic sequence with common difference dd = 3 - 1 = 5 - 3 = 7 - 5 = 2The sum to n terms of an arithmetic sequence is[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][2a + (n - 1)d ]where a is the first termhere a = 1, d = 2, n = 12, hence[tex]S_{12}[/tex] = [tex]\frac{12}{2}[/tex][1 + (11 × 2) ] = 6 [ 2 + (11 × 2) ] = 6 × 24 = 144 → A