3. The answer is either A, B, or C
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
A(n) = –3 + (n – 1)(–2.2)
C. –2.2, –11.8, –19.8
B. –3, –9.6, –22.8
C. –3, –11.8, –25
D. 0, –6.6, –19.8
You know an AP is of the form A(n) = a + (n-1)d
It cannot be A or D, since they do not start with -3
You can see that the common difference is -2.2, so the 4th term must by -3 + 3(-2.2) = -3-6.6 = -9.6
Looks like B to me.
To find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule, we need to plug in the values of n into the sequence's formula and evaluate.
The formula for this arithmetic sequence is A(n) = -3 + (n - 1)(-2.2).
To find the first term, we substitute n = 1 into the formula:
A(1) = -3 + (1 - 1)(-2.2)
= -3 + (0)(-2.2)
= -3 + 0
= -3
Therefore, the first term is -3.
To find the fourth term, we substitute n = 4 into the formula:
A(4) = -3 + (4 - 1)(-2.2)
= -3 + (3)(-2.2)
= -3 + (-6.6)
= -9.6
Therefore, the fourth term is -9.6.
Lastly, to find the tenth term, we substitute n = 10 into the formula:
A(10) = -3 + (10 - 1)(-2.2)
= -3 + (9)(-2.2)
= -3 + (-19.8)
= -22.8
Therefore, the tenth term is -22.8.
Therefore, the first, fourth, and tenth terms of the arithmetic sequence described by the given rule are -3, -9.6, and -22.8 respectively. Among the answer choices provided, option B. -3, -9.6, -22.8 matches the sequence.