Question

The sum of first 26 terms of the AP :10,6,2....... Is

Answer 1

Answer:

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QUESTION :

The sum of first 26 terms of the AP :10,6,2.......

SOLUTION :

Given AP series,

• AP = 10,6,2......

Let, a1 = 10,a2 = 6

Common difference (d) = a2 - a1 = 6 - 10 = -4

➢The common difference (d) is -4

Now we have...

• a = 10
• d = -4
• n = 26
• Sn= ?

Formula : Sn = n/2 [2a + (n-1)d]

• substitute the values..

➡ S26 = 26/2 [ 2(10) + (26 - 1)(-4) ]

➡ S26 = 13 [ 20 + 25(-4) ]

➡ S26 = 13 [ 20 - 100 ]

➡ S26 = 13 [ - 80 ]

➡ S26 = - 104

Therefore,the sum of the AP series is " - 104 " .

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℘ℓḙᾰṧḙ ՊᾰԻк Պḙ ᾰṧ ♭Իᾰ!ℵℓ!ḙṧт ✌✌✌

Answer 2

Answer :-

Given :-

$\large{\rightarrow{\rm{Arithmetic progession = 10 , 6 , 2 \dots }}}$

Required to find :-

• Sum of first 26 terms ?

Formulae used :-

$\Large{\leadsto{\boxed{\sf{ {a}_{nth} = a + ( n - 1 ) d }}}}$

$\Large{\leadsto{\boxed{\sf{ {S}_{nth} = \dfrac{n}{2} [ first \; term + last \; term ] }}}}$

Solution :-

Given :-

A.P = 10 , 6 , 2 , .......

So,

First term = 10

Common difference = ( 2nd term ) - ( 1st term ) = ( 3rd term ) - ( 2nd term )

=> ( 6 - 10 ) = ( 2 - 6 )

=> ( -4 ) = ( -4 )

=> Common difference = - 4

So,

Using the formula let's find the 26th term

$\Large{\leadsto{\boxed{\sf{ {a}_{nth} = a + ( n - 1 ) d }}}}$

Here,

a = first term

d = common difference

n = the term number which you want to find

Hence,

$\rightarrowtail{\tt{ {a}_{nth} = {a}_{26} }}$

$\rightarrowtail{\tt{ {a}_{26} = 10 + ( 26 - 1 ) - 4 }}$

$\rightarrowtail{\tt{ {a}_{26} = 10 + ( 25 ) - 4 }}$

$\rightarrowtail{\tt{ {a}_{26} = 10 + ( - 100 ) }}$

$\rightarrowtail{\tt{ {a}_{26} = 10 - 100 }}$

$\rightarrowtail{\tt{ {a}_{26} = - 90 }}$

26th term = - 90

So,

Using the formula of snth to find the sum of first 26 terms

$\Large{\leadsto{\boxed{\sf{ {S}_{nth} = \dfrac{n}{2} [ first \; term + last \; term ] }}}}$

here,

a = first term

d = common difference

n = the term number which you want to find

Hence,

$\rightarrow{\sf{ {S}_{nth} = {S}{26} }}$

$\rightarrow{\sf{ {S}_{26} = \dfrac{26}{2} [ 10 + ( - 90 ) ] }}$

$\rightarrow{\sf{ {S}_{26} = \dfrac{26}{2} [ 10 - 90 ] }}$

$\rightarrow{\sf{ {S}_{26} = \dfrac{26}{2} [ - 80 ]}}$

$\rightarrow{\sf{ {S}_{26} = 13 \times - 80 }}$

$\rightarrow{\sf{ {S}_{26} = - 1040 }}$

$\Large{\sf{\therefore{Sum \; of \; first \; 26 \; terms = - 1040 }}}$