Question

Find the sum of the first 7 terms of the following series, to the nearest integer. 32, comma, 40, comma, 50, comma, point, point, point 32 , 40 , 50 , . . . 32,40,50,...

Answer 1

The sum of the first 7 terms of the series 32, 40, 50, 62, 76, 92, 110 is determined by adding the numbers together, resulting in a sum of 462.

Step-by-step explanation:

To determine the sum of the first 7 terms of the given series, we need to identify the pattern of the series. This looks like an arithmetic series because each term is increasing by a set amount. The common difference between consecutive terms can be found by subtracting any term from the term that follows it. For instance:

• 40 - 32 = 8
• 50 - 40 = 10

It seems that there is no constant difference, which suggests that this is not a simple arithmetic series. However, the increase from 8 to 10 suggests that the change between terms may be itself increasing, potentially by 2 each time. If this pattern continues the series would look like:

• 32, 40 (32+8), 50 (40+10), 62 (50+12), 76 (62+14), 92 (76+16), 110 (92+18)

Now, to find the sum of the first 7 terms, we simply add them together:

Sum = 32 + 40 + 50 + 62 + 76 + 92 + 110

We can calculate this sum:

Sum = 462

Therefore, the sum of the first 7 terms of the series, to the nearest integer, is 462.

Answer 2

To find the sum of the first 7 terms of the series, one needs to calculate the common difference and apply the formula for the sum of an arithmetic sequence. Assuming a constant increase by the smallest seen step, which is 8, the 7th term is calculated to be 80 and the sum of the first 7 terms is 392.

Step-by-step explanation:

The series presented appears to be an arithmetic sequence because each term increases by a consistent amount. To calculate the sum of the first 7 terms, we need to identify the common difference and use the formula for the sum of the first n terms of an arithmetic series.

First, let's find the common difference by subtracting successive terms:

40 - 32 = 8

50 - 40 = 10

We can see that the common difference is not constant since it varies between 8 and 10, so this is not a strict arithmetic sequence. However, for the purpose of this problem, let's assume it increases by a constant amount, and we'll underestimate using the smallest increase, which is 8 for this sequence approximation.

The formula for the sum of the first n terms of an arithmetic sequence is:

Sₙ= n/2 * (first term + last term)

To find the 7th term, we use the formula for the nth term of an arithmetic sequence:

tₙ= a + (n - 1)d

a is the first term: 32

d is the common difference: 8

n is the term number: 7

Calculating the 7th term:

7 = 32 + (7 - 1)*8 = 32 + 48 = 80

Now, we calculate the sum of the first 7 terms:

7 = 7/2 * (32 + 80) = 3.5 * 112 = 392

To the nearest integer, the sum of the first 7 terms is 392.