Question

find the AP whose 6th term is 25 and 19th term is 77 describe this question solution​

Answer 1

Answer:

firs term = 5

common dif. = 4

AP: 5, 9, 13, 17, ...

Step-by-step explanation:

Let the first term of this AP be a and common difference be d.

   In APs: nth term = a + ( n - 1 )d

⇒ 6th term = 25

⇒ a + ( 6 - 1 )d = 25

⇒ a + 5d = 25   ⇒ a = 25 - 5d

⇒ 19th term = 77

⇒ a + ( 19 - 1 )d = 77

⇒ 25 - 5d + 18d = 77

⇒ 13d = 77 - 25

⇒ 13d = 52

⇒ d = 4

       Hence, a = 25 - 5(4)

                        = 25 - 20

                        = 5

Hence, AP is :

5 , 9 , 13 , 17....

Answer 2

SOLUTION :-

=>6th term is 25, [ Given ]

=>We know nth term of A.P is

=>tn = a+(n-1)d [ Formula ]

• [ putting the values ]

=>so, t6 = a+(6-1)d

=>a+5d=25 -----------(1)

=>t19 = a+18d

=>a+18d=77 -------------(2)

=>subtract equ. 2 from equ. 1

=>we get, -13d = -52

=>d = -52/-13

=>.°. d = 4

=>substitute d=4 in equ. 1

=>a+(5×4)= 25

=>a+20= 25

=>.°. a=5

=>A.P general from is a, a+d, a+2d , a + 3d

=>Therefore , A.P is 5, 9, 13, 17......