What is the common difference of arithmetic sequence 2,8/3, 10/3.write the sequence of integer terms of this sequence.
Answers
common difference is the difference between two terms checking first and second term difference
so common difference=8/3-2=2/3now checking second and third terms
common difference =10/3-8/3=2/3hence common difference Is same
we can terms by using formula
Tn=a+(n-1)d
where a is first term,n is number of term , d is difference
The common difference of the AP is 2/3
The sequence of integer terms of the AP is 2, 4, 6, ...
Given: The AP: 2, 8/3, 10/3, ...
To find:
Common difference of AP
Sequence of integer terms of AP
Solution:
Given AP = 2, 8/3, 10/3,... = 6/3, 8/3, 10/3, ...
Common difference = t₂ - t₁ = t₃ - t₂ = 8/3 - 6/3 = 2/3
∴ The common difference of the AP is 2/3.
Now,
first term = 2
common difference = 6/3
⇒ AP = 6/3, 8/3, 10/3, 12/3, 14/3, 16/3, 18/3, 20/3, ...
Simplifying the terms, we get
AP = 2, 8/3, 10/3, 4, 14/3, 16/3, 6, 20/3, ...
⇒ Sequence of integer terms of AP = 2, 4, 6, ...
∴ The common difference is 2/3 and the sequence of integer terms is 2, 4, 6, ...
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