Question

Math Title:

– Generating Patterns and illustrating Arithmetic Sequence

Determine the common difference and fifth term of the following arithmetic sequence. Provide complete solution in each item...

– Nonsense report –​

Answer 1

9514 1404 393

Answer:

1. 3, 24
2. -7, 37
3. 8, 29
4. -15, 52
5. 9, -17

Explanation:

Since the difference is common, it can be found from the difference of any two terms. It is often easiest to subtract the first term from the second. The 5th term can be found from the 4th by adding the common difference.

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1. d = 15 -12 = 3; a5 = 21 +3 = 24

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2. d = 58 -65 = -7; a5 = 44 -7 = 37

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3. d = 5 -(-3) = 8; a5 = 21 +8 = 29 . . . . note 3rd term is 13, not 1

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4. d = 97 -112 = -15; a5 = 67 -15 = 52

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5. d = -44 -(-53) = 9; a5 = -26 +9 = -17

Answer 2

#1

• Common difference=d=15-12=3
• a=12

`\\ \sf\longmapsto a_5`

`\\ \sf\longmapsto a+4d`

`\\ \sf\longmapsto 12+4(3)`

`\\ \sf\longmapsto 12+12=24`

#2

• d=58-65=-7
• a=65

`\\ \sf\longmapsto a_5=a+4d`

`\\ \sf\longmapsto 65+4(-7)`

`\\ \sf\longmapsto 65-28`

`\\ \sf\longmapsto 37`

#3

• d=5-(-3)=8
• a=-3

`\\ \sf\longmapsto a_5=a+4d`

`\\ \sf\longmapsto -3+4(8)`

`\\ \sf\longmapsto -3+32`

`\\ \sf\longmapsto 29`

#4

• d=97-112=-15
• a=112

`\\ \sf\longmapsto a+4d`

`\\ \sf\longmapsto 112+4(-15)`

`\\ \sf\longmapsto 112-60=52`

#5

• d=-44-(-53)=9
• a=-53

`\\ \sf\longmapsto a+4d`

`\\ \sf\longmapsto -53+4(9)`

`\\ \sf\longmapsto -53+36`

`\\ \sf\longmapsto -17`