Class 11 Mathematics - Chapter Sequence and Series NCERT Solutions | How many terms of the A.P. \begin{align}
How many terms of the A.P. \begin{align} -6, -\frac{11}{2}, -5, ... \end{align} are needed to give the sum –25?
Let the sum of n terms of the given A.P. be –25.
It is known that, \begin{align} S_n = \frac {n}{2}\left[2a + (n -1)d\right]\end{align}, where n = number of terms, a = first term, and d = common difference
Here, a = –6
\begin{align} d = -\frac{11}{2} + 6 = \frac{-11 + 12}{2} = \frac{1}{2}\end{align}
Therefore, we obtain
\begin{align} -25 = \frac {n}{2}\left[2 × (-6) + (n -1)×\frac{1}{2}\right]\end{align}
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