Question

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

Answer 1

a = 38, a₁₆ = 83 a₃₁ = ? 

a_n = a + (n – 1) d 

a₁₆ = a + (16 – 1) d 

a + 15d = 83 

38 + 15d = 83 

15d = 83 – 38 

15d = 45

∴ d = \(\frac{45}{15}\)

∴ d = 3. 

∴ a_n = a + (n – 1)d 

a₃₁ = 38 + (31 – 1) 3 

= 38 + 30 × 3 

= 38 + 90 

∴ a = 128.