Question

find the sum of the following series in Arithmetic progression !
82+80+78+.............+20 ​

Answer 1

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

Answer 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, $S_{n} =?$

Here, first term(a) = 82, common difference(d) = 80 -82 = - 2 and

last term($a_{n}$) = 20

We know that,

$a_{n}=a+(n-1)d$

⇒ $20=82+(n-1)(-2)$

⇒ $20=82-2n+2=84-2n$

⇒ 2n = 64

⇒ n = 32

The sum of the series, $S_{n}=\dfrac{n}{2} (a+a_{n})$

$=\dfrac{32}{2} (82+20)$

$=16\times 102$

= 1632

Hence, the sum of the arithmetic progression is "1632".