Question

16 th term of an Ap is 73 and 11th term in 38 find the common difference and 31st term​

Answer 1

aₙ = a + (n - 1)d is the nth term of Arithmetic Progression.

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 the equations (2) from (1) for the values of a and d.

5d = 35

d = 7

Putting the value of d in the equation (1).

a = 38 - 70

= - 32

31st terms is, a₃₁ = a + (31 - 1)d

= - 32 + 30 × 7

= - 32 + 210

= 178

Answer: The 31st term of AP is 178.

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