Question

Find the sum of first 11 terms of an

A.P is 2, 5, 8,………………​

Answer 1

Answer :

S(11) = 187

Note :

★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.

★ If a1 , a2 , a3 , . . . , an are in AP , then

a2 - a1 = a3 - a2 = a4 - a3 = . . .

★ The common difference of an AP is given by ; d = a(n) - a(n-1) .

★ The nth term of an AP is given by ;

a(n) = a1 + (n - 1)d .

★ The sum of nth terms of an AP is given by ; S(n) = (n/2)×[ 2a + (n - 1)d ] .

or S(n) = (n/2)×(a + l) , where a is the first term , l is the last term and d is the common difference .

Solution :

• Given AP : 2 , 5 , 8 , . . .

• To find : Sum of first 11 terms , S(11) = ?

We have ,

AP : 2 , 5 , 8 , . . .

Clearly ,

• First term , a = 2

• Common difference , d = a2-a1 = 5-2 = 3

Now ,

We know that , the sum of first n terms of an AP is given as ;

S(n) = (n/2)×[ 2a + (n - 1)d ]

Thus ,

The sum of first 11 terms of the AP will be ;

=> S(11) = (11/2)×[ 2a + (11 - 1)d ]

=> S(11) = (11/2)×[ 2a + 10d ]

=> S(11) = (11/2)×2×(a + 5d)

=> S(11) = 11×(a + 5d)

=> S(11) = 11×(2 + 5•3)

=> S(11) = 11×(2 + 15)

=> S(11) = 11×17

=> S(11) = 187

Hence , S(11) = 187 .

Answer 2

Añswèr :

187

Solution :

• Given A.P = 2,5,8,......
• First term , a = 2
• Common difference , d = t2-t1 =>5-2=3
• Sum of 11 terms = ?
• Sum of n terms = n/2 (a+a(n))
• a(n) = a+(n-1)d
• a(11) = 2+(11-1)3
• a(11) = 2+30
• a(11) = 32
• Sum of 11 terms , S(11) = 11/2 (2+32)
• S(11) = 11/2 (34)
• S(11) = 11×17
• S(11) = 187

Therefore sum of 11 terms of given A.P is 187

Note :

• Arithmetic progression : A sequence which has a constant common difference is called as arithmetic progression.

• Common difference : The difference between two successive terms of an A.P is called as common difference.

Important formulàé :

• a(n) = a +(n-1)d , a = first term , d = common difference , a(n) = nth term

• S(n) = n/2 (a+a(n))

(or)

• S(n) = n/2(2a+(n-1)d)

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Students generally get confused between the Quéstìons like , finding the sum of n terms and finding the nth term , kindly don't get confused .

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Therefore required answer is 187