Question

find the sum of first 24 terms of an ap if it is known that a1 +a5+a10+a15+a20+a24=225

Answer 1

Formula's used in calulation:
1) nth term of AP
2) Sum of n terms of AP.

Final result: Sum of first 24 terms of an AP = 900.
Hope , you understand my answer!

Answer 2

Answer: The sum of first 24 terms is 900.

Step-by-step explanation:

Since we have given that

$a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225$

As we know that

$a_n=a+(n-1)d$

so, the above expression becomes,

$a+a+4d+a+9d+a+14d+a+19d+a+23d=225\\\\6a+69d=225\\\\3(2a+23d)=225\\\\2a+23d=\dfrac{225}{3}=75$

So, Sum of first 24 terms would be

$S_{24}=\dfrac{n}{2}(2a+(24-1)d)\\\\S_{24}=\dfrac{n}{2}(2a+23d)\\\\S_{24}=\dfrac{24}{2}(75)\\\\S_{24}=12\times 75=900$

Hence, the sum of first 24 terms is 900.