Analysis of Arithmetic Sequences and Series - Homework

This homework assignment focuses on arithmetic sequences and series. The assignment includes multiple-choice questions, with each question offering a specific problem related to arithmetic sequences. The first problem requires finding the correct sequence based on a formula, while the second problem involves calculating the sum of the first 10 terms of a given sequence. The final problem asks to identify the common difference within an arithmetic sequence. The solutions provided demonstrate the application of formulas and problem-solving techniques relevant to the concepts of arithmetic sequences and series. This assignment is designed to help students understand and apply the principles of arithmetic sequences and series.

1)
Answer:D) 6, 14, 22, 30
The nth term in the sequence is:
an = 8n − 2
The first term then is, that is for n = 1:
a1 = 8 × 1 − 2 = 6
Second term, n = 2:
a2 = 8 × 2 − 2 = 14
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Third term, n = 3:
a3 = 8 × 3 − 2 = 22
Fourth term, n = 4:
a4 = 8 × 4 − 2 = 30
2)
Answer:A) -530
−35, −39, −43, . . .
is a arithmetic sequence with the initialterm: a = −35,and common dif-
ference:d = −39 − (−35) = −43 − (−39) = · · · = −4.
The sum of first n terms in the sequence is given by:
Sn = n
2(2a + (n − 1)d)
Therefore, sum of first 10 terms of the sequence is:
S10 = 10
2 (2 × −35 + 9 × −4) = 5 × −106 = −530
3)
Answer:D) $ 3
The sequence is:
$4, $7, $10, $13, . . .
Common difference ofa arithmetic sequence constant difference between
consecutive terms of the sequence.Here, the difference between terms is:
d = 7 − 4 = 10 − 7 = 13 − 10 = · · · = 3
which is constant.Therefore, the common difference of the sequence is $ 3.
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