NationalEasySequences10–12

Common Difference and Sum of an Arithmetic Sequence

Razão e Soma de uma Sucessão Aritmética

In an arithmetic sequence $(u_n)$ , $u_1 = 7$ and $u_{10} = 34$ . Determine the common difference and the sum of the first $20$ terms.

The gap between two known terms is made up of a whole number of equal steps; count how many steps separate them. The sum formula needs the first and the last term of the block you are adding.

Solution

Step 1 of 4

1.From $u_1$ to $u_{10}$ there are $9$ steps, so $9r = 34 - 7 = 27$ and $r = 3$ .