Question 1006190

For an arithmetic sequence, find t(n) if:
a. t(3)= 6.5 and s(8)=67

b. t(4)={{{ 6/sqrt(5) }}} and s(5)= {{{ 6sqrt(5) }}}

Sorry, I really don't know where to start!!
Please write explanations if you can!
<pre>{{{t[n] = t[1] + (n - 1)d}}}
{{{t[3] = t[1] + (3 - 1)d}}}
{{{6.5 = t[1] + 2d}}}_______{{{t[1] = 6.5 - 2d}}} ------ eq (i)

{{{S[n] = (n/2)(2t[1] + (n - 1)d)}}}
{{{S[8] = (8/2)(2t[1] + (8 - 1)d)}}}
{{{67 = 4(2t[1] + 7d)}}}
{{{67 = 8t[1] + 28d}}} ------------ eq (ii)
{{{67 = 8(6.5 - 2d) + 28d}}} ----- Substituting 6.5 - 2d for {{{t[1]}}} in eq (ii)
{{{67 = 52 - 16d + 28d}}}
67 - 52 = 12d
15 = 12d
{{{15/12 = d}}}, or {{{d = 5/4}}}

{{{t[1] = 6.5 - 2 * (5/4)}}} --------- Substituting {{{5/4}}} for d in eq (i)
{{{t[1] = 6.5 - 5/2}}}
{{{t[1] = 6.5 - 2.5}}}
{{{t[1] = 4}}}

{{{t[n] - t[1] + (n - 1)d}}}
{{{t[n] = 4 + (n - 1)(5/4)}}} ------ Substituting {{{5/4}}} for d, and 4 for {{{t[1]}}} in equation of an AP
{{{t[n] = 4 + (5/4)n - 5/4)}}} 
{{{t[n] = 4 + 5n/4 - 5/4}}}
{{{t[n] = 5n/4 + 2&3/4}}}
{{{highlight_green(t[n] = (5/4)n + 2&3/4)}}}

Apply the same concept to b.