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

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answer is 1.

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Detailed Solution

a₁₁ = 38

a + (11 - 1) d = 38

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

a₁₆ = 73

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

Solving 1 and 2

a + 15d - ( a + 10d ) = 73 - 38

5d = 35

d = 7

Substitute d in equation (1),

a + 10(7) = 38

a = 38 - 70

= - 32

a₃₁ = a + (31 - 1)d

= - 32 + 30 × 7

= - 32 + 210

= 178

Therefore,

31^st term of the AP is 178.

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