Question

if the 9th and 21st term of an ap is a 75 and 183 respectively find its 80 first term

Answer 1

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

Answer 2

hope it is helpful......