The 6th and the 17th tern of an AP are 21 & 54 respectively.Find the 40th term.
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a6 = 21
a17 = 54
an = a +( n - 1) d
a6 = a +(6 - 1) d
21 = a+ 5d............ (i)
a17 = a + ( 17 - 1)d
54 = a + 16d............. (ii)
by substitution method ,
21 - 5d = a.........(iii)
substitute iii in ii
54 = 21 - 5d + 16d
54 - 21 = 11d
33 = 11d
d = 3
substitute d in i
21 = a + 5d
21 = a + 5×3
21 - 15 = a
a = 6
an= a+ ( n -1 )d
a40 = 6 + ( 40 - 1) 3
= 6 + 39×3
= 6 + 117
= 123
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