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Question

Find the sum of first $$16$$ terms of an A.P. $$a_1, a_2, a_3$$,_______.


Solution

Since, 
$$\begin{array}{l} { a_{ 1 } },{ a_{ 2 } },{ a_{ 3 } },.........\, \, are\, \, in\, \, A.P. \\ \therefore \sin  t\, \, term\, a={ a_{ 1 } } \\ Differencel,d={ a_{ 2 } }-{ a_{ 1 } } \\ { S_{ n } }=\frac { n }{ 2 } \left[ { 2a+\left( { n-1 } \right) d } \right]  \\ { S_{ 16 } }=\frac { { 16 } }{ 2 } \left[ { 2{ a_{ 1 } }+\left( { 16-1 } \right) \left( { { a_{ 2 } }-{ a_{ 1 } } } \right)  } \right]  \\ =8\left[ { 2{ a_{ 1 } }+15{ a_{ 2 } }-15{ a_{ 1 } } } \right] =8\left[ { 15{ a_{ 2 } }-13{ a_{ 1 } } } \right]  \end{array}$$

Mathematics

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