Answer:
A
Step-by-step explanation:
The sequence of positive odd numbers is
1, 3, 5, 7, ......
This is an arithmetic sequence with common difference d
d = 3 - 1 = 5 - 3 = 7 - 5 = 2
The 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 term
here 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
Answer:
A. 144.
Step-by-step explanation:
We have been given that a sequence consists of the positive odd integers. We are asked to find the sum of the first 12 terms of the sequence.
Our sequence would be: 1, 3, 5, 7, 9, 11, ....,
We will use sum of sequence formula to solve our given problem.
[tex]S_n=(\frac{a_1+a_n}{2})\cdot n[/tex], where,
[tex]a_1[/tex] = 1st term of sequence,
[tex]a_n[/tex] = nth term of sequence,
[tex]n[/tex] = Number of terms is the sequence.
Let us find nth term of sequence using formula:
[tex]a_n=a+(n-1)d[/tex], where,
d = Difference between two consecutive terms of sequence.
[tex]d=3-1=2[/tex]
[tex]a_n=1+(12-1)2[/tex]
[tex]a_n=1+(11)2[/tex]
[tex]a_n=1+22[/tex]
[tex]a_n=23[/tex]
[tex]S_n=(\frac{1+23}{2})\cdot 12[/tex]
[tex]S_n=24\cdot 6[/tex]
[tex]S_n=144[/tex]
Therefore, the sum of 1st 12 terms of the sequence is 144 and option A is the correct choice.
