Question

Find the sum of the first 25 terms of an arithematic sequence below,12,23,24...

Answer 1

Question:

Find the sum of the first 25 terms of the arithmetic sequence 12,23,34.....

Answer:

$\bigstar{\bold{S_{25}\:=\:1100}}$

Step-by-step explanation:

$\Large{\underline{\underline{\it{Given:}}}}$

• The AP is 12,23,24.......

$\Large{\underline{\underline{\it{To\:Find:}}}}$

• The sum of the first 25 terms of the A.P

$\Large{\underline{\underline{\it{Solution:}}}}$

→ The equation for finding the sum of the sequence is given by

   $\bold{S_n\:=\:\frac{n}{2} \times(a_1+a_n)}$

   where $a_1$ is the first term and $a_n$ is the last term

→ The common difference of the AP = $a_2-a_1$= 23-12 = 11

→ The last term of the AP is given by

   $a_n\:=a_1+(n-1)\times d$

→ Substituting the datas we get,

   $a_n\:=\:12+(25-1)\times 11$

   $a_n\:=\:276$

→ Substitute these datas in the formula for finding the sum

   $S_{25}\:=\:\frac{25}{2}\times(12+276)$

   $\boxed{\bold{S_{25}\:=\:1100}}$

$\Large{\underline{\underline{\it{Notes:}}}}$

• Alternate formula for finding the sum of n terms is given by

• $S_n\:=\:\frac{n}{2} (2a_1+(n-1)\times d)$

       where $a_1$ is the first term of the AP and d is the common          

       difference.