Answer to Question #128759 in Financial Math for Phenyo

Question

Consider the following series: 5 + 8 + 11 + 14 +...+164

1.1.1 Calculate the number of terms in the series. (3)

1.1.2 Calculate the sum of the series. (3)

1.1.3 Express the series in sigma notation.

Answer 1

1.1.1 Calculate the number of terms in the series.

n^th term=a+(n-1)d

where

a is 1^st term,

n is the number of terms,

d is the common difference;

a=5;

d=14-11=11-8=8-5=3;

164=5+(n-1)3

159=3n-3

162=3n

n=54

1.1.2 Calculate the sum of the series.

s_n=ⁿ/₂ [2a+(n-1)d]

where;

s_n is the sum of n terms in the series,

a is 1^st term,

d is the common difference.

s₅₄=⁵⁴/₂ [10+(54-1)3]

s₅₄=27[10+53×3]

s₅₄=27×169

s₅₄=4563

1.1.3 Express the series in sigma notation.

$\displaystyle\sum_{n=1}^{54}(3n+2)$