find the sum of series 31+33+.........+53
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Answer:
51
Step-by-step explanation:
(2(2))3)_(_+_839(_(_8$9)_)_
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Given series is 31+33+...........+53
is in AP
let first term of the AP be a1 =31
second term of the AP be a2=33
and common difference of the AP be d
d=a2-a1
d=33-31
d=2
nthterm of an AP is,
an=a1+(n-1)d
53=31+(n-1)(2)
53-31=2n-2
22 =2n-2
22+2=2n
2n=24
n=24/2
n=12
so 53 is 12th term of the AP.
Sum of the series is,
Sn=n/2[2a1+(n-1)d]
S12=12/2[2×31+(12-1)2]
=12×2/2 [31+11]
=12(42)
=504
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