Maths / Arithmetic Progression / Find Sum of N Terms When Number of terms and Last Term is Given

QUESTION
 

If an AP contains 13 terms and its middle term is 10 . What is the sum of the n terms of the AP ?

EXPLANATION
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Text

n = 13 ;T_7==10;S_n=?;T_7=T_1+6d;T_1=T_7-6d

Similary, T_1+3=T_7+6d;T_1+T_1_3=T_7-6d+T_7+6d=2times T_7

Similarly, T_2+T_1_2=2times T_7;

Adding these, we get

S _n=T_1+T_2+T_3+...+T_7+...T_1_2+T_1_3

Or S_n=(T_1+T_1_3)+(T_2+T_1_2)+(T_3+T_1_1)+...+(T_6+T_8)+T_7

S_n=2T_7+2T_7+2T_7+...+2T_7+T_7

SS_n=2times 6 T_7+T_7=12 times 10 + 10 = 120 + 10 = 130

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