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

Solution:

The n^th term of an Arithmetic progression is given by,

aₙ = a + (n - 1)d 

Here, a is the first term, d is the common difference and n is the number of terms.

aₙ = a + (n - 1)d

a₁₁ = 38

a + (11 - 1) d = 38

a + 10d = 38 ...(1)

a₁₆ = 73

a + 15d = 73 ...(2)

By subtracting equation (1) from equation (2) we get,

a + 15d - ( a + 10d ) = 73 - 38

5d = 35

d = 7

Putting the value of d in equation (1),

a + 10(7) = 38

a = 38 - 70

= - 32

31^st terms is, a₃₁ = a + (31 - 1)d

= - 32 + 30 × 7

= - 32 + 210

= 178

The 31^st term of the AP is 178.

☛ Check: NCERT Solutions Class 10 Maths Chapter 5

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Video Solution:

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

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 7

Summary:

The 31^st term of an AP whose 11^th term is 38 and the 16^th term is 73 is 178.

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