Question

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

Answer 1

Answer:

• 31st term of AP is 178

Step-by-step explanation:

Given : 11th term of AP = 38 and 16th term of AP = 73

To find : 31st term of AP

Solution:

In this question, concept of elimination method and concept of AP is used. We are given 11th term and 16th term of AP and we are asked to find the 31st term. To get the value of 31st term, firstly we have to find the common difference and first term of AP. We can use the given statements and apply elimination method to find the value of common difference and by substituting value of common difference, we can get value of first term. Then it will be véry easy to find 31st term by using first term and common difference. So let's proceed by creating equations for given statements.

Given 11th term of AP can also be expressed as:

→ a₁₁ = a +10d

Here,

• a=First term

• d =common difference

• a₁₁=11th term of AP

→ 38 = a + 10d    ...(1.)

Given 16th term of AP can also be expressed as:

→ a₁₆ = a + 15d

→ 73 = a + 15d    ...(2.)

Applying elimination method or subtract equation (1.) from (2.)

→ 73 - 38 =  a + 15 d -( a + 10d)

→ 35 = a + 15d - a - 10d

→ 35 = a - a + 15d - 10d

→ 35 = 5d

→ 35/5 = d

→ 7 = d

Now put this value of d in equation (1.)

→ 38 = a + 10d

→ 38 = a + 10(7)

→ 38 = a + 70

→ 38 - 70 = a

→ -32 = a

Now, to find 31st term, we can express it as::

a₃₁ = a + 30d

a₃₁ = -32 + 30 (7)

a₃₁ = -32 + 210

a₃₁ = 178

So the required 31st term of AP is 178.