Question

In an ap the 10 th term is 46 sum of 5 th and 7 th term is 52 find the ap​

Answer 1

Answer:

The required A.P is 1, 6, 11, 16 ...

Step-by-step explanation:

nth term of an A.P is given by,

$\bf a_n = a + (n-1) d$

where

a is the first term

d is the common difference

_____________________

10th term = 46

a + (10 – 1)d = 46

a + 9d = 46

a = 46 – 9d

____________

5th term + 7th term = 52

a + (5 – 1)d + a + (7 – 1)d = 52

2a + 4d + 6d = 52

2a + 10d = 52

2(a + 5d) = 2(26)

a + 5d = 26

Put a = 46 – 9d,

46 – 9d + 5d = 26

46 – 4d = 26

4d = 46 – 26

4d = 20

d = 20/4 = 5

Common difference = 5

_________________

Finding the first term,

a = 46 – 9(5)

a = 46 – 45

a = 1

Second term :

= a + d

= 1 + 5

= 6

Third term :

= a + 2d

= 1 + 2(5)

= 1 + 10

= 11

Fourth term :

= a + 3d

= 1 + 3(5)

= 1 + 15

= 16

Therefore, the A.P is 1, 6, 11, 16 ...

Answer 2

Answer:

16 is the answer mate........