the sum of 5th and 9th terms of an arithmetic progression is 40 and the sum of 8 and 14 term is 60 find sum of first 20 terms
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AP. Formula = a+(n - 1)(d)
5th term = a+ (5-1)d
a+4d
9th term = a+(9-1)d
a+8d
their Sum;
a+4d+a+8d = 40
2a+12d = 40 _____(i)
8th term = a+(8-1)d
a+7d
14 th term = a+(14-1)d
a+13d
their Sum ;
a+7d+a+13d = 64
2a + 20d = 64 ______(ii)
By subtracting equations (i) and (ii)
2a+20d = 64
2a+12d = 40
8d = 24
d = 24/8
⇝ d = 3
their for a = 2a+20(3)=64
2a + 60 = 64
2a = 64-60
2a = 4
a = 4/2
⇝a = 2
we got a as 2 and d as 2
so,
sum of 20 th term ;
n/2 { 2a + n -1 d }
20/2 { 2(2) + (20-1)(2)}
10 { 4 + 19(2)}
10 ( 4+ 38 )
10(42)
420
Hence, the Sum of 20th term is 420.
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