Question

the 9th term of an ap is 99 and the 99th term is 9 find the general term and sum of its 20 term

Answer 1

A9 = a + 8d
99 = a + 8 d. ........(1)
A99 = a + 98 d
9 = a + 98d .'.........(2)

add 1 &2
-90d = 90
D = -1
A + 8d = 99
A + (-8) = 99
A = 99 + 8
A = 107

a9= A + ( n - 1 ) d
99 = 107 + ( n - 1 ) -1
-6 = ( n - 1 ) -1
n = 7
an = a + ( n - 1 ) d
an = 107 + ( 7 - 1 ) -1
an = 107 + (-6)
an = 107 - 6
an = 101

S20 = 20/2(107 + 101 )
= 10 (208)
= 2080


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