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JEE Mains · Maths · STD 11 - 8. sequence and series
If \(a_1 , a_2, a_3, . . . . , a_n, ....\) are in \(A.P.\) such that \(a_4 - a_7 + a_{10}\, = m\), then the sum of first \(13\) terms of this \(A.P.\), is .............. \(\mathrm{m}\)
- A \(10\)
- B \(12\)
- C \(13\)
- D \(15\)
Answer & Solution
Correct Answer
(C) \(13\)
Step-by-step Solution
Detailed explanation
If \(d\) be the common differnce, then \(m = {a_4} - {a_7} + {a_{10}} = {a_4} - {a_7} + {a_7} + 3d = {a_7}\) \({S_{13}} = \frac{{13}}{2}\left[ {{a_1} + {a_{13}}} \right] = \frac{{13}}{2}\left[ {{a_1} + {a_7} + 6d} \right]\)…
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