Math CentralQuandaries & Queries


Question from Abbi:

hi there im a student in 11 grade

ive been trying to do this task but i have no idea how to do it
the question is
Find the common difference and the n^th term of the arithmetic sequence if the first term is 4 and the twentieth sum of the terms is 1030


I think the problem says

the first term is 4 and the sum of the first twenty terms is 1030

If the common difference is $d$ then here are a few of the terms

first term second term third term ....... twentieth term
$4$ $4+d$ $4+2d$ ..... $4+19d$

The sum of these terms is 1030 so

\[4 + (4+d) + (4+2d) + \cdot \cdot \cdot + (4 + 19 d) = 1030.\]

which simplifies to

\[20 \times 4 + d(1 + 2 + \cdot \cdot \cdot + 19) = 1030.\]

Solve for $d.$


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