Identify the 25th term of the arithmetic sequence 2, 1 and 3 over 5, 1 and 1 over 5 …

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 369 People

Identify the 25th term of the arithmetic sequence 2,1 (3 / 5), 1 ( 1 / 5) ... (2 points)

Answered by maham237 @ 25/12/2020

Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial value, d=common difference, n=term number.

The common difference is the constant difference found by subtracting the previous term from any term. In this case:

d=2-1 3/5=1 3/5-1 1/5=-2/5=-0.4 and we can easily see that the first term is 2 so

a(n)=2-0.4(n-1) which can be simplified...

a(n)=2-0.4n+0.4

a(n)=2.4-0.4n, so the 25th term is:

a(25)=2.4-0.4(25)

a(25)= -7.6 or if you prefer...

a(25)= -7 3/5

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