find the sum of the following series in Arithmetic progression !
82+80+78+.............+20
Answers
Answered by
6
Answer:
1632
Step-by-step explanation:
given
a= 82
d= -2
an= 20
n=?
sn=?
an= a+(n-1)d
20= 82+(n-1)-2
20= 82+ (-2n)+2
20-84= -2n
-64/-2= n
n= 32
sn= n/2 (2a+(n-1)d
sn= 32/2 (2*82 + (32-1) -2
sn= 16 ( 164 + 31*(-2)
sn= 16 (164-62)
sn= 16*102
sn= 1632
Answered by
2
The sum of the arithmetic progression is "1632".
Step-by-step explanation:
The given series in srithmetic progression:
82 + 80 + 78 +.............+ 20
To find, the sum of the series,
Here, first term(a) = 82, common difference(d) = 80 -82 = - 2 and
last term() = 20
We know that,
⇒
⇒
⇒ 2n = 64
⇒ n = 32
The sum of the series,
= 1632
Hence, the sum of the arithmetic progression is "1632".
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