Question

Find the sum of the first 10 terms of the arithmetic sequence: 5, 12, 19,26,...

Answer 1

S₁₀ = 365

Step-by-step explanation

The sum of the first n terms of an arithmetic sequence is called the arithmetic series formula,

`S_n=(n(a_1+a_n))/(2)`

In this sequence, we can see that the first term a₁ is 5. To find the sum of the first 10 terms of the sequence, we have to use n = 10, so we have to find a₁₀.

The nth term of an arithmetic sequence is,

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

To find the common difference, d, we have to use any term of the given sequence. With n = 2, we use a₂

`a_2=12=5+d(2-1)`

Solving for d,

`\begin{gathered} 12=5+d \\ d=12-5=7 \end{gathered}`

Thus, the formula for the nth term of this sequence is,

`a_n=5+7(n-1)`

So now we can find the 10th term,

`a_(10)=5+7(10-1)=5+7\cdot9=5+63=68`

And the sum of the first 10 terms,

`S_(10)=(10(5+68))/(2)=(10\cdot73)/(2)=(730)/(2)=365`

Hence, the sum of the first 10 terms of this arithmetic sequence is 365.