Question

determine the Ap whose third term is 16 and 17th term exceds the 5th term

Answer 1

i)a+2d=16. . . (1)

ii) a+6d=a+4d+12
2d=12
d=6 in (1)
a+2(6)=16
a=4

therefore the ap is 4,10,16,. . .

I hope it helps you. . .

Answer 2

Question:

   

Determine the AP whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.

Answer: 4, 10, 16,...

       

           

Step-by-step explanation:

       

If the 7th term exceeds the 5th term by 12, then the difference of 7th term and 5th term is 12.

$a_7-a_5=12 \\ \\ \Rightarrow\ (7-5)d=12 \\ \\ \Rightarrow\ 2d=12 \\ \\ \Rightarrow\ d=6$

$a_3-a_1=(3-1)d \\ \\ \Rightarrow\ 16-a_1=2 \times 6 \\ \\ \Rightarrow\ 16-a_1=12 \\ \\ \Rightarrow\ a_1=16-12 \\ \\ \Rightarrow\ a_1=4 \\ \\ \\ a_2=a_1+d \\ \\ \Rightarrow\ a_2=4+6 \\ \\ \Rightarrow\ a_2=10$

So the AP is 4, 10, 16,...

Plz ask me if you have any doubts.

Thank you. :-))

#adithyasajeevan