Verify the identity. Please show your work.
1 answer:
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The given sequence is
a₁, a₂, ...,
Because the given sequence is an arithmetic progression (AP), the equation satisfied is
where
d = the common difference.
The common difference may be determined as
d = a₂ - a₁
The common difference is the difference between successive terms, therefore
d = a₃ - a₂ = a₄ - a₃, and so on..
The sum of the first n terms is
Example:
For the arithmetic sequence
1,3,5, ...,
the common difference is d= 3 - 1 = 2.
The n-th term is
For example, the 10-term is
a₁₀ = 1 + (10-1)*2 = 19
Th sum of th first 10 terms is
S₁₀ = (10/2)*(1 + 19) = 100
a₁, a₂, ...,
Because the given sequence is an arithmetic progression (AP), the equation satisfied is
where
d = the common difference.
The common difference may be determined as
d = a₂ - a₁
The common difference is the difference between successive terms, therefore
d = a₃ - a₂ = a₄ - a₃, and so on..
The sum of the first n terms is
Example:
For the arithmetic sequence
1,3,5, ...,
the common difference is d= 3 - 1 = 2.
The n-th term is
For example, the 10-term is
a₁₀ = 1 + (10-1)*2 = 19
Th sum of th first 10 terms is
S₁₀ = (10/2)*(1 + 19) = 100