Question

Maths class 10
find the sum of A.p 34+32+30 - - +10​

Answer 1

Answer:

The sum of given AP= 286

Step-by-step explanation:

Here, a(first term)= 34   ;   d(common difference)= 32 - 34= -2

l(last term) =10

So, these values will provide us the sum of  given AP!!!

Prior to this we have to find 'n' value  (n = no. of terms in AP)

To find n:

l = a+(n-1)d

10=34+(n-1) -2

10=34 - 2n + 2

-2n = 10-36

-2n = -26   (minus gets cancelled)

n=13   (Therefore, the given AP has 13 terms!)

To find sum:

We use the formula,  S= n/2 (a+l)         (since last term is known)

S= n/2 (a+l)           (S=sum)

S=  13/2 (34 + 10)

S= 13/2 (44)

S= 13 x 22

S= 286( ans.)

Hope it helps :)

All the best!!

Answer 2

a1 = 34 , d= a2-a1 , an =10

an = a + ( n - 1 )d

10 = 34+( n - 1 )-2

10 = 34 - 2 n + 2

10 = 34 + 2 - 2n

10 =36 - 2n

10 - 36 = - 2n

-26 = -2n

n = 26/2

n= 13

Sn = n/ 2 ( 2a + ( n -1)d

S13 = 13/2 ( 2(34) + (13 - 1 ) -2 )

= 13/2 ( 68 + ( -24) )

= 13/2 (44) ( Here 2 is cutting 44 = 22 )

= 13 x 22

= 286