Question

*
1 point
The sum of first 24 terms of the AP an+az+az.
if it is known that
as+as+a1o+as+azo+a24=225 is.......
O (a)500
O (b)600
O (c)900
O (d)100​

Answer 1

Answer:

(c)900

Step-by-step explanation:

Given; a  1 +a  5  +a  10 +a  15  +a 20 +a  24  =225

(a  1 +a  24  )+(a  5 +a  20 )+(a  10  +a 15  )=225    ...(1)

Let first term is a and common difference is d then

a  1  =a,a  24  =a+23d,⇒a  1  +a  24  =2a+23d    ...(2)

a  5  =a+4d,a  20  =a+19d,⇒a  

5 +a  20  =2a+23d   ...(3)

a  10 =a+9d,a  15  =a+14d,⇒a  

10 +a  15  =2a+23d   ...(4)

Putting (2),(3),(4) in (1), we get

3(2a+23d)=225⇒2a+23d=75   ...(5)

Now a  1  +a  2  +a  3 +a  4  +...+a  24  =524

⇒524=  2 24  [2a+(24−1)d]=12(2a+23d)   ...(6)

From (5) and (6)

  =12×75=900