Asequence 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

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

= [2a + (n - 1)d ]

where a is the first term

here a = 1, d = 2, n = 12, hence

= [1 + (11 × 2) ]

                         = 6 [ 2 + (11 × 2) ]

                        = 6 × 24 = 144 → A

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.

, where,

= 1st term of sequence,

= nth term of sequence,

= Number of terms is the sequence.

Let us find nth term of sequence using formula:

, where,

d = Difference between two consecutive terms of sequence.

Therefore, the sum of 1st 12 terms of the sequence is 144 and option A is the correct choice.