Question

Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.

Answer 1

Answer:

The sum of n terms of an A.P. is n [2 - 3n]

Step-by-step explanation:

Given :  

nth terms of an A.P. , an = 5 − 6n …….(1)

 

On putting n = 1 in eq 1,

an = 5 − 6n

a1 = 5 – 6(1)  

a1 = 5 – 6  

a1 = -1

On putting n = 2 in eq 1,

a2 = 5 – 6(2)  

a2 = 5 – 12  

a2 = -7

Common Difference , d = a2 - a1

d = -7 + 1 = -6

d = -6

First term , a = -1

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

Sn = n/2 [2(-1) + (n -1) (-6)]

Sn = = n/2 [2(-1) -6n + 6]

Sn = = n/2 [-2 + 6 - 6n]

Sn = = n/2 [4  - 6n]

Sn = n/2 × 2 [2 -  3n]

Sn = n [2 - 3n]

Hence, the sum of n terms of an A.P. is n [2 - 3n]

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Answer 2

Step-by-step explanation:

an = 5 − 6n

a1= 5 - 6×1= - 1

a2= 5 - 6×2 = - 7

a3 = 5 - 6×3 = -13

Difference (d) = -13-(-7)= - 6

Sum of n term = n/2 ( first term + last term)

Sum of n term = n/2 ( - 1+ 5 − 6n)

Sum of n term = n/2 ( 4− 6n)

Sum of n term = n (2-3n)

Sum of n term = 2n - 3n² Ans