Question

please give me the answer step by step please help me ​

Answer 1

Answer:

give thanks

Step-by-step explanation:

3).5,8,11,14....

A=5

D=8-5=3

25th term = a+24d

5+24(3)

5+72

77

Answer 2

Answer :

$\large{\star\:\:\boxed{\bf{S_{25}\:=\:1025}}\:\:\star}$

Question :–

Find the Sum of first 25 terms of an arithmetic sequence 5, 8 , 11 , 14 ,...

Explanation :

Given :–

• 5 , 8 , 11 , 14 ,...
• where a = 5 and d = 3 .

To Find :–

S₂₅ (Sum of first 25 terms)

Formula Applied :–

• $\boxed{\star\:\:\bf{S_{n}\:=\:\dfrac{n}{2}\:[2a\:+\:(n\:-\:1)d] }\:\:\star}$

Solution :–

We have ,

• a = 5
• d = 3
• n = 25

Putting these values in the Formula :

$\rightarrow\sf{S_{n}\:=\:\dfrac{n}{2}\:[2a\:+\:(n\:-\:1)d] }$

$\rightarrow\sf{S_{25}\:=\:\dfrac{25}{2}\:[2(5)\:+\:(25\:-\:1)(3)] }$

$\rightarrow\sf{S_{25}\:=\:\dfrac{25}{2}\:[10\:+\:(24\:\times\:3)] }$

$\rightarrow\sf{S_{25}\:=\:\dfrac{25}{2}\:(10\:+\:72) }$

$\rightarrow\sf{S_{25}\:=\:\dfrac{25}{2}\:\times\:82 }$

$\rightarrow\sf{S_{25}\:=\:25\:\times\:41 }$

$\rightarrow\boxed{\bf{S_{25}\:=\:1025}}$

∴ The Sum of first 25 terms is 1025 .