the 6th term of ana.p. is 19 and 17th term is 41.find the 40th term
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the 14 th term of an ap= a + 13 d
= 9 + 2×39= 78+ 9 =87
= 9 + 2×39= 78+ 9 =87
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a6 = 19
a + 5d = 19 ..... ( i ).
a17 = 41
a + 16d = 41. . ... ( ii )
Sub ( ii ) from ( i )
a + 5d - ( a + 16d ) = 19 - 41
a + 5d - a - 16d = - 22
- 11d = - 22
d = 2
Putting in ( i )
a + 5d = 16
a + 10 = 16
a = 6
To find 40th term
a40 = a + 39d
a40 = 6 + 39 × 2
a40 = 6 + 78
a40 = 84
a + 5d = 19 ..... ( i ).
a17 = 41
a + 16d = 41. . ... ( ii )
Sub ( ii ) from ( i )
a + 5d - ( a + 16d ) = 19 - 41
a + 5d - a - 16d = - 22
- 11d = - 22
d = 2
Putting in ( i )
a + 5d = 16
a + 10 = 16
a = 6
To find 40th term
a40 = a + 39d
a40 = 6 + 39 × 2
a40 = 6 + 78
a40 = 84
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