Question

​In an ap consists of 43 terms, if the sum of 5 middle most term is 195, then sum of ap is ?​

Answer 1

Answer:

Step-by-step explanation:

For elements in AP..

a1 = a  

a2 = a + d

a3 = a + 2d

a4 = a + 3d

...

if the sum of 5 middle most term is 195.

Middle term in AP - (43 + 1)/2 = 22

a20 + a21 + a22 + a23 + a24 = 195

(a + 19d) + (a + 20d) + (a + 21d) + (a + 22d) + (a + 23d) = 195

5a + 19d + 20d + 21d + 22d + 23d = 195

5a + 105 d = 195

Therefore, a + 21 d = 39 --- (1)

Now sum of ap :- a1 + a2 + a3.. a43

= a + (a+d) + (a+2d) + .... (a+ 42d)

= 43a + (42.43/2)d

= 43a + 903d

= 43 ( a + 21d)

Substituting from 1 we get,

= 43 x 39 = 1677