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Sagot :
Arithmetic Sequence:
The first term of the sequence is 26 and the common difference is 6.
Definition:
An arithmetic sequence is a sequence of numbers such that the difference of any two succeeding terms of the sequence is a constant while an arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, a and last term, an, divide by 2 in order to get the mean of the two values and then multiply by the number of values.
Step by Step Solution:
- Write the given.
S = 530 (sum of the first 10 terms of the arithmetic sequence)
a = 80 (10th term of the arithmetic sequence)
- Identify what is asked.
a = ____ (first term of the arithmetic sequence)
d = ____ (common difference of the arithmetic sequence)
- Identify the formula to be used.
a = a + (n – 1)d
S = [2a + (n – 1)d]n/2
- Write the solution.
a = a + (10 – 1)d
80 = a + 9d
- Rename the equation to a by adding -9d to both sides of the equation. Thus, 80 + (-9d) = a + 9d + (-9d) which when simplified is 80 – 9d = a
- Substitute the derived equation for a in the equation for the sum of the arithmetic sequence to solve for the common difference.
S = [2a + (n – 1)d]n/2
530 = [2(80 – 9d) + (10 – 1)d]10/2
530 = [160 – 18d + 9d]5
530 = [160 – 9d]5
530 = 800 – 45d
- Combine the similar terms.
530 + (-800) = – 45d
- Divide both sides by -45 to solve for d.
6 = d . Therefore, the common difference is 6.
- Now, find the first term of the arithmetic sequence using the formula: 80 – 9d = a
80 – 9(6) = a
80 – 54 = a
26 = a . Therefore, the first term of the arithmetic sequence is 26.
For more information regarding arithmetic sequence, read the following links:
https://brainly.ph/question/825249
https://brainly.ph/question/600653
https://brainly.ph/question/651839
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