Question

the 13th term of an ap is 4 times it's 3rd term . if its 5th term is 16, find the sum of it's first 10 terms​

Answer 1

Answer:

$s(10)=175$

Step-by-step explanation:

Since

$T(13)=4×T(3)$

$T(5)=16$

We Know That

$a(n)=a+(n-1)d$

So,

$→a(13)=a+12d$

$→a(3)=a+2d$

By solving this, we get,

$→a+2d=4a+8d$

$→a=\frac{4}{3}×d$

Also,

$→a(5)=a+4d=16$

Putting value of a,

we get,

$→d=3$

also,

$→a=4$

we know,

$→s(n)=\frac{n}{2}×(a(1)+a(n))$

$→a(10)=4+(9×3)=31$

$→s(10)=5×(4+31)=\boxed{175}$