If aₘ denotes mth term of an A.P. then aₘ =

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8. Sequences and Series

easy

If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =

A

$\frac{2}{{{a_{m + k}} + {a_{m - k}}}}$

B

$\frac{{{a_{m + k}} - {a_{m - k}}}}{2}$

C

$\frac{{{a_{m + k}} + {a_{m - k}}}}{2}$

D

None of these

Solution

(c) ${a_{m + k}} = A + (m + k – 1)\,D$

and ${a_{m – k}} = A + (m – k – 1)\,D$

Adding both equations, we get

$\frac{{{a_{m + k}} + {a_{m – k}}}}{2} = A + (m – 1)\,D = {a_m}$.

Standard 11

Mathematics

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