Q. 143.7( 12 Votes )

# Determine the AP whose third term is 16 and the 7^{th}term exceeds the 5^{th}term by 12.

Answer :

Given

a_{3} = 16; a_{7} = a_{5} + 12

a + (7-1) d = a + (5-1) d +12

2d = 12

d = 12

Common difference (d) = 12

Substituting value of d in a_{3}

a_{3} = 16

a + (3-1) d = 16

a + 2 (6) = 16

a = 4

∴ The series will be a, a+d, a+2d, a+3d,….

4, 10, 16, 22,…

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