Question

find the sum of 25 term of the arithmetic sequences 5,8,11​

Answer 1

Given :-

The series in A.P are 5, 8 , 11 . . .

To find :-

• Sum of 25 terms

SOLUTION:-

We have formulae to find the sum of n terms in A.P that is

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

Where ,

• S_n = Sum of n terms
• n = no.of terms
• d = common difference
• a = first term

So,

Lets find first value of a, n , d in given series

5 , 8 , 11 . . .

First number is 5 (a)

Common difference =

• 8- 5 = 3
• 11 - 5 = 3

Common difference is 3

Number of terms is 25

i.e

• a = 5
• d = 3
• n = 25

Substituting the values in formula

$S_n = \: \dfrac{25}{2} 2(5) + (25 - 1)(3)$

$S_n = \dfrac{25}{2} [10 + 24(3)]$

$S_n = \dfrac{25}{2}(10 + 72)$

$S_n = \dfrac{25}{2}(82)$

$S_n = 25(41)$

$S_n = 1025$

So,

$\red { \boxed{ \: Sum \: of \: \: 25 \: \: terms \: in \: given \: \: A.P \: is \: 1025}}$

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Answer 2

Given :-

The series in A.P are 5, 8 , 11 . . .

To find :-

Sum of 25 terms

SOLUTION:-

We have formulae to find the sum of n terms in A.P that is

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

Where ,

S_n = Sum of n terms

n = no.of terms

d = common difference

a = first term

So,

Lets find first value of a, n , d in given series

5 , 8 , 11 . . .

First number is 5 (a)

Common difference =

8- 5 = 3

11 - 5 = 3

Common difference is 3

Number of terms is 25

i.e

a = 5

d = 3

n = 25

Substituting the values in formula

$S_n = \: \dfrac{25}{2} 2(5) + (25 - 1)(3)$

$S_n = \dfrac{25}{2} [10 + 24(3)]$

$S_n = \dfrac{25}{2}(10 + 72)$

$S_n = \dfrac{25}{2}(82)$

$S_n = 25(41)$

$S_n = 1025$

So,

$\red { \boxed{ \: Sum \: of \: \: 25 \: \: terms \: in \: given \: \: A.P \: is \: 1025}}$

Know more similar Question in brainly :-

https://brainly.in/question/40767511