Question

find the first term and the 20th term of an ap whose 5th and 7th term are 13 and 17

Answer 1

here is your answer hope it is correct

Answer 2

HEY BUDDY..!!!

HERE'S THE ANSWER..

_____________________

♠️ a5 = 13 and a7 = 17 , We have to find a20

⏺️ Now for solving this type of questions , refer the following way.

⏺️We know { an = a + ( n - 1 ) d }

⏺️ a5 = a + 4 d

⏺️a7 = a + 6 d

✔️ a + 4 d = 13_______( 1 )

✔️ a + 6 d = 17_______( 2 )


▶️ Now by ( 2 ) - ( 1 )

=> a + 6 d = 17

=> a + 4 d = 13
( - ) ( - ) ( - )

_____________
=> 2 d = 4
_____________

✔️ [ d = 2 ] ✓ // common difference ( d )


⏺️ Now putting value of d in eqn ( 1 )

⏺️a + 4 d = 13

=> a + 4 ( 2 ) = 13

=> a + 8 = 13

=> a = 13 - 8

=> [ a = 5 ]✓


♠️ Now similarity { a20 = a + 19 d }

=> a20 = a + 19 d

=> a20 = 5 + 19 ( 2 )

=> [ a20 = 43 ]✔️✔️


HOPE HELPED..

JAI HIND..

:-)