Question

Determine the sum of the first 7 terms of the arithmetic sequence with

general formula t_n = -3n +7

Answer 1

your answer is -35.

Explanation:

let the first 7 terms be 1,2,3,4,5,6, and 7.

we have ,

general term t_n = -3n +7 ,then

t_1 = -3*1 +7

= -3+7

= 4

t_2 = -3*2 +7

= -6 +7

= 1

t_3 = -3*3 +7

= -9+7

= -2

t_4 = -3*4 +7

= -12+7

= -5

t_5 = -3*5 +7

= -15+7

= -8

t_6 = -3*6 +7

= -18+7

= -11

t_7 = -3*7 +7

= -21+7

= -14

Now, the sum of first seven terms is

4 + 1 + (-2) + (-5) + (-8) + (-11) + (-14)

= 5 -2 - 5 - 8 - 11 - 14

= -35

Answer 2

-35

Explanation:

Sum of the first 7 terms of AP is:

• S_7= 1/2*7(t_1 + t_7)

As per general formula t_n= -3n +7 we find the first and seventh terms and the sum of the first 7 terms:

• t_1= - 3*1 + 7= 4
• t_7= - 3*7 + 7= - 14
• S_7 = 7/2*(4-14)= 7/2*(-10)= - 35

Answer is - 35