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 *a*1 and the typical difference is *d*, climate the *n*th 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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Algebra 2Sequences and also series: Binomial theorem

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SEQUENCES AND series – Geometric sequences and also series

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