the 13th term of an ap is 4 times its third term if the 5th term is 16 then find the sum of the first 10 terms
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T(13)= 4*T(3)
T(5)=16
as we know a(n)=a+(n-1)d
so a(13)=a+12d
a(3)=a+2d
equating.....
a+12d=4a+8d
we get,
a=(4/3)*d
also,a(5)=a+4d=16
putting value of a we get,
d=3
also a=4
as we know,
sum(n)=(n/2)*(a(1)+a(n))
a(10)=4+(9*3)=31
sum(10)=5*(4+31)=175......which is the answer....
hope this helps...
T(5)=16
as we know a(n)=a+(n-1)d
so a(13)=a+12d
a(3)=a+2d
equating.....
a+12d=4a+8d
we get,
a=(4/3)*d
also,a(5)=a+4d=16
putting value of a we get,
d=3
also a=4
as we know,
sum(n)=(n/2)*(a(1)+a(n))
a(10)=4+(9*3)=31
sum(10)=5*(4+31)=175......which is the answer....
hope this helps...
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