Question 1135959
For the series 16, 24, 36, 54,... find S7.
<pre>That person is WRONG, as usual! This is NOT an A.P. with 4 as the common difference. It is in fact a G.P. with r or the common ratio being 1.5.
You can use the formula for a specific term in a G.P. to find the last term, or ({{{matrix(1,3, a[n], "=", a[1]r^(n - 1))}}}), where: r is 1.5, and a<sub>1</sub>, or 1st term is 16.
Last term: {{{matrix(2,3, a[7], "=", 16(1.5)^(7 - 1), a[7], "=", 182.25)}}}
Sum of a G.P.: {{{matrix(1,3, S[n], "=", (a[1] - a[n] * r)/(1 - r))}}}, where: n = 7     ;      a<sub>1</sub>, or 1st term = 16     ;     a<sub>n</sub>, or LAST term = 182.25      ;       r = 1.5
Sum of the 1st 7 terms of this G.P.: {{{highlight_green(matrix(3,3, S[7], "=", (16 - 182.25(1.5))/(1 - 1.5), S[7], "=", (- 257.375)/(- .5), S[7], "=", highlight(514.75))))}}}