Question

in an ap the the third tem is four times the first tems and 6th term is 17 find the series

Answer 1

Hey user

Here is your answer :-

In an A.P.

We know that

tn = a + ( n - 1 )d

t3 = a + ( 3 - 1 )d

t3 = a + 2d

By the given condition

t3 = 4a

a + 2d = 4a

- 3a + 2d = 0 ... ( 1 )

t6 = a + ( 6 - 1 )d

17 = a + 5d. ... ( 2 )

Multiplying equation ( 2 ) by 3 we get

3a + 15d = 51. ... ( 3 )

Adding equations ( 1 ) & ( 3 ) we get

- 3a. + 2d = 0
+
3a + 15d = 51
______________
0 + 17 d = 51

17 d = 51

d = 3

Putting d = 3 in equation ( 1 )

- 3a + 2 ( 3 ) = 0

-3a + 6 = 0

3a = 6

a = 2

Si the required A.P is 2 , 5 , 8 ...