Question

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

Answer 1

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Answer 2

Given :

• a₁₁ = 38
• a₁₆ = 73

To find :

• a₃₁ = ?

Solution :

We know that,

• aₙ = a + (n – 1)d

Therefore,

• a₁₁ = a + 10d = 38⠀⠀⠀–––––(1)
• a₁₆ = a + 15d = 73⠀⠀⠀–––––(2)

Subtracting ( 1 ) from ( 2 ),

→ a + 15d - a - 10d = 73 - 38

→ 5d = 35

→ d = 7

Substituting the value of 'd' in ( 1 ),

→ a₁₁ = a + 10d = 38

→ a + 10 × 7 = 38

→ a + 70 = 38

→ a = 38 - 70

→ a = -32

Now 31st term,

→ a₃₁ = a + 30d

→ a₃₁ = -32 + 30 × 7

→ a₃₁ = -32 + 210

→ a₃₁ = 178

•°• The 31st term of the AP is 178.