Question

A sequence consists of the positive odd integers. What is the sum of the first 12 terms of the sequence?

Answer 1

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

$S_{n}$ = $\frac{n}{2}$[2a + (n - 1)d ]

where a is the first term

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

$S_{12}$ = $\frac{12}{2}$[1 + (11 × 2) ]

                         = 6 [ 2 + (11 × 2) ]

                        = 6 × 24 = 144 → A

Answer 2

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.

$S_n=(\frac{a_1+a_n}{2})\cdot n$, where,

$a_1$ = 1st term of sequence,

$a_n$ = nth term of sequence,

$n$ = Number of terms is the sequence.

Let us find nth term of sequence using formula:

$a_n=a+(n-1)d$, where,

d = Difference between two consecutive terms of sequence.

$d=3-1=2$  

$a_n=1+(12-1)2$

$a_n=1+(11)2$

$a_n=1+22$

$a_n=23$

$S_n=(\frac{1+23}{2})\cdot 12$

$S_n=24\cdot 6$

$S_n=144$

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