Find \(S_{17}\) if \(a_4=-15\) and \(a_9=-30\).
\(S_{17}=-510\)
Step 1: Recall formulas.
Step 2: Write equations using given terms.
We know:
Step 3: Subtract the equations to find \(d\).
(ii) – (i):
\((a + 8d) - (a + 3d) = -30 - (-15)\)
\(5d = -15\)
So, \(d = -3\).
Step 4: Substitute \(d\) in equation (i) to find \(a\).
\(a + 3(-3) = -15\)
\(a - 9 = -15\)
\(a = -6\).
Step 5: Use the sum formula for \(n = 17\).
\(S_{17} = \dfrac{17}{2}[2a + (17-1)d]\)
\(= \dfrac{17}{2}[2(-6) + 16(-3)]\)
\(= \dfrac{17}{2}[-12 - 48]\)
\(= \dfrac{17}{2}[-60]\)
\(= 17 \times -30\)
\(= -510\).
Final Answer: \(S_{17} = -510\)