Find the 31st term of an AP whose 11th term is 38 and 16th term is 73. Class 9

Find the 31^st term of an AP whose 11^th term is 38 and 16^th term is 73. Class 9

Question 1.

Find the 31^st term of an AP whose 11^th term is 38 and 16^th term is 73. Class 9

Solution:

Given, t_n = 38, t₁₆ = 73

t_n = a + (n -11) d

For n = 11,

t₁₁ = a +10 d

∴ 38 = a + 10d ... (i)

For n = 16,

t₁₆ = a +15 d

∴ 73 = a + 15d ...(ii)

Subtracting (i) from (ii), we get

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

∴ 5d = 35

∴ d = 7

Substitute d = 7 in (i),

a + 10 (7) = 38

∴ a + 70 = 38

∴ a = -32

Now, for n = 31

t₃₁ = a + 30d

= -32 + 30 x 7

= -32 + 210

∴ t₃₁ = 178.

∴ 31^st term of AP is 178.