Question

Plz Solve. I am in puzzled.

Answer 1

10th term = 46
=> a + 9d = 46 ------------(eq1)

Sum of 5th and 7th term = 52
=> (a+4d) + (a+6d) = 52
=> 2a + 10d = 52 -----------------(eq2)

Multiply eq1 with 2, we get
2a + 18d = 92 ---------------------(eq3)

Subtract eq2 from eq3, we get
(2a + 18d) - (2a + 10d) = 92-52
=> 8d = 40
=> d = 40/8 = 5

a = 46 - 9d = 46 - 9×5 = 46-45 = 1

AP has a = 1 and d=5

AP = 1, 6, 11, 16...

Answer 2

Answer:

1,6,11,16

Step-by-step explanation:

nth term of AP a(n) = a + (n - 1) * d.

(i) 10th term of an AP is 46:

a₁₀ = a + (10 - 1) * d

46 = a + 9d

(ii) Sum of 5th and 7th terms is 52:

a₅ + a₇ = 52

a + (5 - 1) * d + [a + (7 - 1) * d] = 52

a + 4d + a + 6d = 52

2a + 10d = 52

a + 5d = 26

On solving (i) & (ii), we get

a + 9d = 46

a + 5d = 26

----------------

     4d = 20

         d = 5.

Substitute d = 10 in (i), we get

a + 9d = 46

a + 9(5) = 46

a + 45 = 46

a = 46 - 45

a = 1.

Hence, Required A.P is a, a + d, a + 2d, a+3d, .... which is 1,6,11,16.

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

Hope this helps!