Determine the AP whose third term is 16 and whose 7th term exceeds the 5th term by 12. Class 9

Determine the AP whose third term is 16 and whose 7^th term exceeds the 5^th term by 12. Class 9

Question 1.

Determine the AP whose third term is 16 and whose 7^th term exceeds the 5^th term by 12. Class 9

Solution:

t₃ = 16

∴ a + 2d = 16 ... (i)

7^th term exceeds the 5^th term by 12,

∴ t₇ = t₅ + 12

∴ t₇ - t₅ = 12

∴ (a + 6d) - (a + 4d) = 12

∴ 2d = 12

∴ d = 6

Substitute d = 6 in (i),

a + 2 (6) = 16

∴ a + 12 = 16

∴ a = 4

∴ The AP is 4, 10, 16, 22,...