Question

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

Answer 1

ANSWER

S₁₀ = 365

EXPLANATION

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

$S_n=\frac{n(a_1+a_n)}{2}$

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,

$S_{10}=\frac{10(5+68)}{2}=\frac{10\cdot73}{2}=\frac{730}{2}=365$

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