Question 1016403

the 4th term of an A.P is 15 and the 9th term is 35. Find the fifteenth term?
<pre><b><u>4<sup>th</sup> term</u></b>
{{{a[n] = a[1] + (n - 1)d}}}
{{{a[4] = a[1] + (4 - 1)d}}}
{{{15 = a[1] + 3d}}} ------- eq (i)

<b><u>9<sup>th</sup> term</u></b>
{{{a[n] = a[1] + (n - 1)d}}}
{{{a[9] = a[1] + (9 - 1)d}}}
{{{35 = a[1] + 8d}}} ------- eq (ii)

- 20 = - 5d ------ Subtracting eq (ii) from eq (i)
d, or common difference = {{{(- 20)/(- 5)}}}, or 4
{{{35 = a[1] + 8(4)}}} ------- Substituting 4 for d in eq (i)
{{{35 = a[1] + 32}}}
{{{matrix(1,8,a[1], or, 1^st, term, "=", 35 - 32, or, 3)}}}

{{{a[n] = a[1] + (n - 1)d}}}
{{{a[15] = 3 + (15 - 1)4}}} ------- Substituting 15 for n, 3 for {{{a[1]}}}, and 4 for d
{{{a[15] = 3 + 14(4)}}}
{{{highlight(highlight_green(highlight(matrix(1,8,a[15], or, 15^th, term, "=", 3 + 56, or, 59))))}}}