Question

find the 31st term of an AP whose 11th term is 38 and 16th term is 73​

Answer 1

Answer:

178

Step-by-step explanation:

11th term=a+10d=38. eqn 1

16 th term= a+15d=73. eqn 2

solving eqn 1 and 2, we get

d= 7, a= -32

31st term= a+30d= 178

Answer 2

Answer:

The 31st term of the AP is 178.

Step-by-step explanation:

Given:

11th term of AP = 38

16th term of AP = 73

To find:

The question is to find the 31st term of the AP

Solution:

The formula to find the nth term of an AP is given as follows,

  Tₙ = a + (n-1)d

Where 'a' is the first term and 'd' is the common difference of an AP.

Therefore,

  T₁₁ = a + 10d = 38  →  (1)

  T₁₆ = a + 15d = 73  →  (2)

Now subtract equation (1) from equation (2) ⇒

    a + 15d - (a + 10d ) = 73 - 38

    a + 15d - a - 10d = 35

          5d = 35

           $d=\dfrac{35}{5} \\\\d=7$

Substitute the value 'd' in equation (1) to find the first term⇒

  a + 10(7) = 38

  a + 70 = 38

   a = 38 - 70

      = -32

Then the 31st term of the AP ⇒

T₃₁ = a + 30d = -32 + 30(7)

            = -32 + 210

            = 178

Hence the 31st term of the AP is 178.