Question

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

Answer 1

Answer:

1025

Step-by-step explanation:

$\frac{n}{2} \times (2a + (n - 1)d)$

here

n means 25

a means 5

d means 3

Answer 2

Given :–

• Arithmetic terms 5 , 8 , 11 , 14..
• Where a = 5 and d = 3

Need To Find Out :–

• Sum of first 25 terms,S₂₅ =?

Solution :–

As we know the formula for finding sum of an arithmetic sequence given by :-

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

Where:-

• a = 5
• d = 3
• n = 25

Now, Put these values in the Formula :-

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

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

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

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

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

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

$:\implies \red {\boxed{\sf{S_{25}\:=\:1025}}}$

$\sf\therefore{\underline{Hence\: ,the \: Sum \: of\: first\: 25\: terms \: is \: \red{\bold{1025}.}}}$