Question

If the first term of an AP is -5 and the common difference is 2,then the sum of the first 6 terms is (a) 0,(b) 5,(c) 6,(d) 15​

Answer 1

HEYA MATE !

a = (-5)

d= (2)

S6 = n/2 {a +( a +(n-1)d)}

S6= 6/2 {(-5)+((-5)+(6-1)2}

S6= 3{ (-5)+(-5+10)}

S6= 3 {-5 -5+10}

S6= 3 × 0

S6= 0

hope it helps

Answer 2

Answer:

Required sum of 6 terms of the given AP is 0.

Step-by-step explanation:

It is given that the first term of an AP is -5 and the common difference is 2.

From the properties of arithmetic progressions :

• S${}_n=\dfrac{n}{2}$[ 2a + ( n - 1 ) d ] , where a is the first term, n is the number of terms, d is the common difference between the terms and S${}_n$ is the sum of n terms.

Thus, comparing the question, substituting the values

= > S₆ = ( 6 / 2 ){ 2( - 5 ) + ( 6 - 1 )( 2 ) }

= > S₆ = 3{ - 10 + 5( 2 ) }

= > S₆ = 3{ -10 + 10 }

= > S₆ = 3 x 0

= > S₆ = 0

Hence the required sum of 6 terms of the given AP is 0.