Find the sum of the first 17 terms of arithmetic sequence 2,5,8
Answer (1)
The sum of the first 17 terms is 442.ExplanationGivenFirst term (a) = 2Common difference (d) = 5 − 2 = 3Number of terms (n) = 17Formula for the sum of the first n terms of an arithmetic sequence:[tex] \sf \: S_{n} = \dfrac{n}{2} [2a + (n - 1)d][/tex]Substitute the values:[tex]\sf \: S_{17} = \dfrac{17}{2} [2(2) + (17 - 1)3] \\ \\ = \sf \dfrac{17}{2} [4 + (16) (3)] \\ \\ = \sf \dfrac{17}{2} [4 + 48] \\ \\ = \sf \dfrac{17}{2} \times 52 \\ \\ = \sf \dfrac{884}{2} \\ \\ \boxed{ \sf = 442}[/tex]
