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
Explain TypeExplanation Content
Text

n = 13 ;$\dpi{100} T_7==10;S_n=?;T_7=T_1+6d;T_1=T_7-6d$

Similary, $\dpi{100} T_1+3=T_7+6d;T_1+T_1_3=T_7-6d+T_7+6d=2\times T_7$

Similarly, $\dpi{100} T_2+T_1_2=2\times T_7;$

Adding these, we get

$\dpi{100} S _n=T_1+T_2+T_3+...+T_7+...T_1_2+T_1_3$

Or $\dpi{100} S_n=(T_1+T_1_3)+(T_2+T_1_2)+(T_3+T_1_1)+...+(T_6+T_8)+T_7$

$\dpi{100} S_n=2T_7+2T_7+2T_7+...+2T_7+T_7$

S$\dpi{100} S_n=2\times 6 T_7+T_7=12 \times 10 + 10 = 120 + 10 = 130$

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