Question

Write the sum using summation notation, assuming the suggested pattern continues.

-4 + 5 + 14 + 23 + ... + 131

Answer 1

@jdoe0001

Answer 2

so -4, + 5, + 14, + 23, + ... + 131

so it starts off at -4
ends at +131

from -4 to +5 is 9 units so that'd be our "d" "common difference"
since is an "arithmetic" sequence

so.... what's 131? well.. .we dunno
but we know -4 and "d"
so \(\bf a_{\color{brown}{ n}}=a_1+({\color{brown}{ n}}-1){\color{blue}{ d}}\implies a_{\color{brown}{ n}}=-4+({\color{brown}{ n}}-1){\color{blue}{ 9}}
\\ \quad \\
\textit{so what's term is it with 131?}
\\ \quad \\
131=-4+({\color{brown}{ n}}-1){\color{blue}{ 9}}\implies 131=-4+9n-9\implies 131=-13+9n
\\ \quad \\
131+13=9n\implies \cfrac{\cancel{ 144 }}{\cancel{ 9 }}=n\)

Answer 3

n=16