An arithmetic succession is a succession of numbers such the the difference of any two succeeding members that the sequence is a constant.

You are watching: Which of the following is an arithmetic sequence?

Example

2,4,6,8,10….is an arithmetic sequence v the common difference 2.

If the very first term of an arithmetic succession is a1 and the typical difference is d, climate the nth term of the sequence is provided by:

$$a_n=a_1+(n-1)d$$

An arithmetic series is the amount of one arithmetic sequence. We uncover the amount by including the first, a1 and last term, an, divide by 2 in order to gain the median of the two values and then main point by the variety of values, n:

$$S_n=fracn2(a_1+a_n)$$

Example

Find the amount of the complying with arithmetic series 1,2,3…..99,100

We have a complete of 100 values, for this reason n=100. Our an initial value is 1 and our critical is 100. We plug these values right into our formula and also get:

$$S_100=frac1002(1+100)=5050$$

Video lesson

Find the 20th worth of the adhering to sequence 1,4,7,10….

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