Question

Find the sum of a finite arithmetic sequence from n=1 to n=5 using the expression -3(4)^n-1

Answer 1

Explanation:

Arithmetic sequaence:

`\sf a_n = -3(4)^n - 1\\\\a_1=-3*4^1 -1\\\\ = -3*4 - 1\\\\ = -12 - 1\\\\a_1=-13`

`a_2 = -3*4^2-1\\`

= -3*16 -1

= -48 - 1

= -49

difference = second term - first term

= -49 -(-13)

= -49 + 13

d = -36

`\boxed{S_n=(n)/(2)[2a + (n-1)d]}`

`\sf S_5=(5)/(2)*[2*(-13} + 4*(-36)]\\\\ =(5)/(2)[-26-144]\\\\=(5)/(2)*(-270)`

= 5*(-135)

= -675