Question

seventh term of an arithmetic sequence is 10 and the 10th term is 17. what is it's 17th term​

Answer 1

Given :-

$a_7=10\\a_{10}=17$

Required to find :-

$a_{17}=?$

What need to be used :-

• Ability of solving 2 simultaneous linear equation.
• $a_n=a+(n-1)d$    

Procedure :-

$a_7=a+6d=10\\a+6d=10$------ 1

$a_{10}=a+9d=17\\a+9d=17$-----2

By subtracting 1 from 2, we get

$a-a+9d-6d=17-10\\3d=7\\d=\frac{7}{3}$

Let us substitute in 1.

$a+14=10\\a=-4$

Now let us finally find 17th term.

$a_{17}=a+16d\\a_{11}=-4+\frac{112}{3} \\a_{11}=\frac{100}{3}$