Question

find the eleventh term from the last term of the A.P 27,23,19,.......,_65.

Answer 1

Heya,
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Let the first term of AP be 'a'
i.e a=27
Let the common difference between two consecutive terms of an AP be 'd'
i.e d= 23-27 = -4
Let the last term(nth term) be tn
i.e an=-65
Acoording to the formula,
an= a+(n-1)*d
=> -65=27+(n-1)(-4)
=> -65=27-4n+4
=> 4n=27+4+65
=> 4n=96
=> n=24
n denotes the number of terms in AP
Now let us find 11th term
a11=27+(11-1)(-4)
a11=27-40
a11= -13
The answer is -13

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hope this helped u,
cheers

Answer 2

AP: 27,23,19,.....,-65
just writing the given AP in reverse order ,
AP: -65,.....,19,23,27
so a=-65 ,d= 27-23=4,
11th term= a+ (n-1)d
                 = -65+(11-1)4
                 = -65+10×4    
                =  -65+40=-25
                   ⇒11th term of this AP=-25