[tex]ARITHMETIC \: \: PROGRESSIONS \\ \\ \\
Given \: arithmetic \: series \: - \\ \\ 17 \: , \: 24 \: , \: 31 \: , \: 38 \: , .... \\ \\ Let \: \: the \: first \: term \: be \: \: A \: \\ A \: \: = \: \: 17 \\ \\ Common \: difference \: \: = \: \: D \\ D \: \: = \: \: A2 - A1 \: \: = 24 - 17 = 7 \\ \\ ( \: An \: denotes \: nth \: term \: of \: the \: series \: ) \\ \\ We \: know \: that \: , \\ \\ An \: = \: A + (n - 1)D \\ \\ A40 = 17 + 39D \\ \\ A40 = 17 + 39 \times 7 = 17 + 273 \\ \\A40 = 290 \\ \\ \\ Let \: Sn \: denotes \: sum \: of \: n \: terms \: of \: the \\ \: series \\ \\ Sn = \frac{n}{2} (A + An) \\ \\ S40 = \frac{40}{2} (17 + 290) \\ \\ S40 = 20 \times 307 \\ \\ \\ S40 = 6140 \: \: \: \: \: \: \: \: Ans.[/tex]
