Question

If nth term of an AP is 7 - 4n. Find the sum of first five terms.

Answer 1

Answer:

-25

Step-by-step explanation:

nth term=7-4n

1st term=7-4=3

2nd term=7-4*2=-1

common difference=-1-3=-4

S(n)=n/2(2a+(n-1)d)

      =5/2(6+4*-4)

      =5/2(-10)

      =-25

conceptual explanation:

from the given nth term, we try to find the first and the second term; by putting n=1, n=2 respectively. Then from their difference we get the common difference of the AP.

now we have the first term, common difference and the number of terms whose sum is to be found. so, we can easily substitute the values in the formula and get the required answer.

Answer 2

Answer:

AP = 7-4n

let , n = 1  

so, a =  7-4(1)

a= 3

n= 2

so, 7-4n

==> 7-4(2) => 7-8 ==> -1

so, a = 3 , d= -1-3 ==> -4

so, SUM OF FIRST FIVE TERM

==> S = 1/2[ 2A+(N-1)D]

==> S = 1/2[2(3)+(5-1)-4]

==> 1/2[6+4(-4)]

==> 1/2[6-16]

==> 1/2[-10]

SUM OF FIVE TERM==> -5