Question

common difference of AP is -2 . find the sum when first term is 100 and last term is -10​

Answer 1

given, d = -2

        a = 100

       l or $a_n$  = - 10  

first we have to find the total no. of terms , n = ?

==> $a_n$  = a +  ( n - 1 )  d

from given, we put the values,

==> -10 = 100 + ( n - 1 )  ( - 2 )

==> -10 - 100  = -2n + 2

==> -110  - 2 =  -2n

==> -112 / -2  = n

==> 56 = n

using sum formula to get the total sum of the terms,

==> $S_5_6$  =  $\frac{n}{2} ( 2a + (n - 1)d)$

here, n = 56 , a = 100 and d = -2

==> $S_5_6 = \frac{56 }{2 } { 2 (100 ) + (56 - 1) (-2) }$

==>S56 = 28 [200 -110]

==> s56 = 28 x 90

==> S56 = 2320

hope u got ur answer......

Answer 2

Answer:

given, d = -2

a = 100

l or a_na

n

= - 10

first we have to find the total no. of terms , n = ?

==> a_na

n

= a + ( n - 1 ) d

from given, we put the values,

==> -10 = 100 + ( n - 1 ) ( - 2 )

==> -10 - 100 = -2n + 2

==> -110 - 2 = -2n

==> -112 / -2 = n

==> 56 = n

using sum formula to get the total sum of the terms,

==> S_5_6 = \frac{n}{2} ( 2a + (n - 1)d)

2

n

(2a+(n−1)d)

here, n = 56 , a = 100 and d = -2

==> S_5_6 = \frac{56 }{2 } { 2 (100 ) + (56 - 1) (-2) }

==>S56 = 28 [200 -110]

==> s56 = 28 x 90

==> S56 = 2320