if the 9th and 21st term of an ap is a 75 and 183 respectively find its 80 first term
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an = a1 + (n - 1)d
Given that the 9th term is 75
75 = a + 8d
Given that 21st term is 183
183 = a + 20d
Put the two equations together:
75 = a + 8d ------------------ [ 1 ]
183 = a + 20d ------------------ [ 2 ]
[ 2 ] - [ 1 ]:
108 = 12d
d = 108 ÷ 12
d = 9
FInd a:
75 = a + 8d
75 = a + 8(9)
75 = a + 72
a = 75 - 72
a = 3
Find the nth term:
an = a1 + (n - 1)d
an = 3 + (n - 1)9
an = 3 + 9n - 9
an = 9n - 6
Find the 80th term:
an = 9n - 6
an = 9(80) - 6
an =720 - 6
an = 714
Answer: 714
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hope it is helpful......
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Friendship11:
is answer right
yes
in eqn 2 you have written 183 but while subtracting u have written 180
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