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