Question

1)Find the sum of the arithmetic sequence.

-10, -7, -4, -1, 2, 5, 8
a)11
b)-70
c)0
d)-7
2)Find the sum of the geometric sequence.
1, 1/4, 1/16,1/64,1/256
a)341
b)1/192
c)1/768
d)341/256
3)Write the sum using summation notation, assuming the suggested pattern continues.
-9 - 4 + 1 + 6 + ... + 66
4)Write the sum using summation notation, assuming the suggested pattern continues.
25 + 36 + 49 + 64 + ... + n2 + ...
5)Write the sum using summation notation, assuming the suggested pattern continues.
8 - 40 + 200 - 1000 + ..
6)Find the sum of the first 12 terms of the sequence. Show all work for full credit.
1, -4, -9, -14, . . .

Answer 1

See below

Explanation:

1) Sum = (n/2){a1 + L] where n = number count, a1 = first term and L = last term

so here its is (7/2) [ -10 + 8]

= 7/2 * -2

= -7 (answer)

2/

Sum of n terms = a1 * (1 - r^n)/ (1 - r) where r = common ratio

Here r = 1/4

so its 1 * ( 1 - 1/4^5) / 1 - 1/4

= 341 / 256

3.

This is an arithmetic sequence with first term -9, last term 66 and common difference 5.

16

∑ (-9 + 5(n - 1)

n=1

Note the 16 comes from 66 being the 16th term ( solve 66 = -9 + 5(n - 1)

5 This is geometric with common ratio -5 , first term 8 which continues without bounds.

∞

∑ 8(-5)^(n-1)

n=1

6. This is arithmetic with a1 = 1 and d = -5

Sn = (n/2) [ 2a1 + (n - 1)d]

So S12 = 6( 2 + 11*-5)

= 6 * -53

= -318 ( answer)