Question

if 5 terms the fifth term of an ap is equal to the 8 times its eighth term, show that 13 term is zero

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Answer 1

$\huge \fbox{ \underline \blue{Answer }}$

Given:

5 times the 5th term = 8 times the 8th term

Let us denote it in terms of Arithmatic Progression.

Formula for arithmatic progression (Sn) terms is

$\pink{ \boxed{S_{n}\:=\: a+(n-1)d }}$

Here,

a = First term

d = Common Difference

Now,

5a₅ = 8a₈

5[a+(5-1)d] = 8[a+(8-1)d]

5[a+4d] = 8[a+7d]

5a+20d = 8a+56d

-3a = 36d

a = -12d -------> equation 1

$\green{ \boxed{a\: = -12d }}$

Now Sn for 13th term,

S₁₃ = [a+(13-1)d]

     = [a + 12d]

     = [ -12d + 12d ] {substituting the value of "a"}

S₁₃ = 0

Hence proved.

Hope it helps

Refer same question at,

https://brainly.in/question/1076372

Answer 2

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