Respuesta :
Answer:
The sixteenth term is (7.5y - 6.5x).
Step-by-step explanation:
The first term of the A.P. is given to be x and the common difference is assumed to be d.
So, the third term = y = x + (3 - 1)d {Given that the third term is y}
Then, 2d = y - x
⇒ [tex]d = \frac{y - x}{2}[/tex]
Therefore, the sixteenth term of the A.P. will be = x + (16 - 1)d
= [tex]x + 15 \times \frac{y - x}{2}[/tex]
= x + 7.5y - 7.5x
= 7.5y - 6.5x (Answer)
Answer:
The sixteenth term is [tex]x+\frac{15(y-x)}{2}[/tex].
Step-by-step explanation:
Given,
[tex]a_1=x[/tex]
[tex]a_3=y[/tex]
And also given, [tex]T_n=a+(n-1)d[/tex]
We have to find out the 16th term of given A.P.
Firstly, we will find out the common difference(d).
Common difference(d) is calculated by given formula.
[tex]T_3=a+(n-1)d[/tex]
On putting the values, we get;
[tex]y=x+(3-1)d\\\\y=x+2d\\\\2d=y-x\\\\d=\frac{y-x}{2}[/tex]
Now the value of 'd' is calculated, so we can find out the 16th term by using the formula.
[tex]T_{16}=x+(16-1)\frac{y-x}{2}\\\\T_{16}=x+15\times\frac{y-x}{2}\\\\ T_{16}=x+\frac{15(y-x)}{2}[/tex]
Hence The sixteenth term is [tex]x+\frac{15(y-x)}{2}[/tex].
