1. 31,38,45
2. -17, -29, -41
3. -2, 3, 8, 13, 18
4. -2, 3, 8, 13
Step-by-step explanation:
1. Find the next 3 terms of the arithmetic sequence. Write your answers with commas but no spaces. 3,10,17,24
First of all we have to find the common difference of the sequence
So,
[tex]d = a_2 - a_1 = 10-3 = 7\\d = a_3-a_2 = 17-10 = 7[/tex]
D = 7 so recursive formula will be:
[tex]f(n) = f(n-1)+7[/tex]
So for next three terms
[tex]f(5) = f(4) + 7 = 24+7 = 31\\f(6) = f(5) + 7 = 31+7 = 38\\f(7) = f(6) + 7 = 38 + 7 = 45[/tex]
2. Find the next 3 terms of the arithmetic sequence. Write your answers with commas but no spaces. 31,19,7,-5
First of all we have to find the common difference of the sequence
So,
[tex]d = a_2 - a_1 = 19-31 = -12\\d = a_3 - a_2 = 7-19 = -12[/tex]
As d = -12, the recursive formula will be:
[tex]f(n) = f(n-1) -12\\So,\\f(5) = f(4) - 12 = -5-12 = -17\\f(6) = f(5) - 12 = -17-12 = -29\\f(7) = f(6) -12 = -29-12 = -41[/tex]
3. Find the first 4 terms of the Arithmetic sequence. Write your answers with commas but no spaces.
f(n) = f(n-1) + 5
f(1) = -2
[tex]f(2) = f(1) +5 = -2+5 = 3\\f(3) = f(2) + 5 = 3+5 = 8\\f(4) = f(3) +5 = 8+5 = 13\\f(5) = f(4) +5 = 13+5 = 18[/tex]
4. Write the first 3 numbers of the sequence. Write your answers with commas but no spaces.
f(n) = f(n-1) + 5
f(1) = -2
[tex]f(2) = f(1) +5 = -2+5 = 3\\f(3) = f(2) + 5 = 3+5 = 8\\f(4) = f(3) +5 = 8+5 = 13[/tex]
Keywords: Arithmetic Sequences, common difference
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