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An arithmetic sequence has t1=5 and t2=8 find tn and sn

User Mrmannione
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1 Answer

6 votes

Answer:


a_n=2+3n


\displaystyle S_n=(7n+3n^2)/(2)

Explanation:

Arithmetic Sequences

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:


a_n=a_1+(n-1)r

Where

an = nth term

a1 = first term

r = common difference

n = number of the term

The sum of the n terms of an arithmetic sequence is given by:


\displaystyle S_n=(a_1+a_n)/(2)\cdot n

We are given the first two terms of the sequence:

a1=5, a2=8. The common difference is:

r = 8 - 5 = 3

Thus the general term of the sequence is:


a_n=5+(n-1)3=5+3n-3=2+3n


\boxed{a_n=2+3n}

The formula for the sum is:


\displaystyle S_n=(5+2+3n)/(2)\cdot n


\displaystyle S_n=(7+3n)/(2)\cdot n

Operating:


\boxed{\displaystyle S_n=(7n+3n^2)/(2)}

User Cgogolin
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