Question

The 14th term of an AP is twice the 8th term , if the 6th term is -8 then find the sum of it's first 20 terms

Answer 1

Answer:

A14=2a8 and a6=-8 a20=?

u can find it know

Answer 2

Sum of first 20 term is:

Step-by-step explanation:

$\ Given \ value:\\\\ \ 14^{th} term = a+13d \\\\\ 8^{th} term = a+7d\\\\ a+13d = 2( a+7d)....................(i)\\\\ \ 6^{th} term( a+5d)\ = -8 ...................(ii)\\\\\ Solve \ equation \ (i)..\\\\ a+13d = 2( a+7d) \\\\a+13d= 2a+14d\\\\2a-a+14d-13d=0\\\\a+d=0...........(iii)\\\\\ subtract \ equation \ (ii) \ to (iii) ...\\\\ a+5d\ = -8 \\\\ - \\ a+d=0 \\\\4d=-8\\\\d=-2\\\\\ put \ the \ value \ of \ d \ in \ equation \ (ii)...\\\\a+5(-2) = -8\\\\a-10=-8\\\\a=10-8 \\\\a= 2$

$\ a= 2 , \ d = -2 , n= 20.\\\\\ Formula \ to \ find \ sum\\\\S_n =\frac{n}{2}[2a+(n-1)d]\\\\\ Solution:\\\\S_n=\frac{20}{2}[2\times2+(20-1)-2]\\\\S_n= 10[2\times2+19\times-2]\\\\S_n= 10[4-38]\\\\S_n= 10[-34]\\\\S_n=-340$

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• Finding Sum: https://brainly.in/question/14346820