If five times the fifth term of an AP is equal to 8 times the 8th term, value of 13th term is...

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26 Apr 2013 AP If five times the fifth term of an AP is equal to 8 times the 8th term, value of 13th term is...: OPtion
1) -2
2) -1
3) 0
4) 2
5) 5
6) 10
7) 12
8) 15
9) 17
10) None of these; Correct Option: 3 Best Solution (8)

Sagar Jinachandran 11 years AGO

5(a+4d)=8(a+7d)
5a+20d=8a+56d
-3a=36d
a=-12d
so 13th term=a+12d
=>-12d+12d=0
option 3

Like? Yes (15) | No (8)

Anita 11 years AGO

Taking simple case, when 5th term =8 and 8th term is 5, then d=-1 and a=12
then 13 th term = 12-12=0

Like? Yes (9) | No (6)

dan 11 years AGO

5th term is ->a+4t [a=first term,t=diff b/w consecutive terms]
8th term is ->a+7t
5(a+4t)=8(a+7t)
=>a=-12t
13th term is=a+12t
=>-12t+12t=0 (Ans.)

Like? Yes (9) | No (7)

krishnapriya 11 years AGO

Let 'a' be first term and 'd' be common difference.
Given 5a5=8a8
5(a+4d)=8(a+7d)(since an=a+(n-1)d)
5a+20d=8a+56d
a=-12d
a+12d=0-----------(1)

a13=a+12d=0 (using (1))
Therefore, value of 13th term is zero.

Like? Yes (6) | No (4)

Darpankumar 11 years AGO

since we know the nth term= a1+(n-1)d
so 5th term will be= a1+(5-1)d
so 8th term will be= a1+(8-1)d
and 5*[a1+(5-1)d]=8*[a1+(8-1)d]
solving this we get
a1=-12d
let d=1
than the terms will be

-12,-11,...........-1,0(13th term);

Like? Yes (7) | No (6)

M Rakesh 11 years AGO