Question

the sum of 5th and 7th term of an AP is 52 and the 10th term is 46 find the AP.

Answer 1

a10 = a + 9d = 46

a5 + a7 = 52

a+4d+a+6d = 52

2a + 10 d = 52

a + 5d = 26

solve a10 and this equation...



4d = 20

d = 5

a+ 25 = 26

a= 1

so, ap is 1,6,11,16,21,26...

Answer 2

5th term = a + 4d

7th term = a + 6d

According to the question :

a + 4d + a + 6d = 52

2a + 10d = 52

2 ( a + 5d ) = 52

a + 5d = 52 / 2

a + 5d = 26 ----- equation 1)

a + 9d = 46 ------ equation 2)

a = 26 - 5d ------- equation 3)

Put equation 3 in 2

26 - 5d + 9d = 46

26 + 4d = 46

4d = 46 - 26

4d = 20

d = 20 / 4

d = 5

a + 9d = 46

a + 9 ( 5 ) = 46

a + 45 = 46

a = 46 - 45 = 1

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

Hope it helps you :-)