Question

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

Answer 1

Answer:

$a_n=2+3n$

$\displaystyle S_n=\frac{7n+3n^2}{2}$

Step-by-step 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:

$\displaystyle S_n=\frac{a_1+a_n}{2}\cdot n$

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:

$\displaystyle S_n=\frac{5+2+3n}{2}\cdot n$

$\displaystyle S_n=\frac{7+3n}{2}\cdot n$

Operating:

$\boxed{\displaystyle S_n=\frac{7n+3n^2}{2}}$