Answer:
First term: a
Second term: a+d
Third term:a+2d
Step-by-step explanation:
An expression that can model the first three terms of any arithmetic sequence in terms of just a and d is aₙ = a + (n - 1)d.
An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 8, 13, 18, and 23 is 5. An arithmetic progression is another name for an arithmetic sequence.
Let the a be the initial term of a sequence and d be the common difference, then the nth term of any arithmetic sequence can be written as aₙ = a + (n - 1)d.
If we want first three terms of any arithmetic sequence, then we have to put n = 1, 2, 3 in the above expression.
So, for n = 1, a₁ = a + (1 - 1)d = a + 0d = a
for n = 2, a₂ = a + (2 - 1)d = a + d
for n = 3, a₃ = a + (3 - 1)d = a + 2d
Therefore, an expression that can model the first three terms of any arithmetic sequence in terms of just a and d is aₙ = a + (n - 1)d.
Learn more about arithmetic sequences here -
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