Question 1150834
The sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms of the sequence is -165.find the 18th term of the sequence
<pre>Sum of "n" terms of an A.P.: {{{matrix(1,3, S[n], "=", (n/2)(2a[1] + (n - 1)d))}}}
{{{matrix(1,3, S[10], "=", (10/2)(2a[1] + (10 - 1)d))}}} ------- Substituting 10 for n
{{{matrix(1,10, - 60, "=", 5(2a[1] + 9d), "=====>", 2a[1] + 9d, "=", - 12, "-------", eq, (i))}}} ------ Substituting - 60 for {{{S[10]}}}

{{{matrix(1,3, S[15], "=", (15/2)(2a[1] + (15 - 1)d))}}} ------- Substituting 15 for n
{{{matrix(1,3, - 165, "=", 15(2a[1] + 14d)/2)}}} ------------- Substituting - 165 for {{{S[15]}}}
{{{matrix(1,10, 15(2a[1] + 14d), "=", - 330, "____", 2a[1] + 14d, "=", - 22, "-----", eq, (ii))}}}
5d = - 10 ------- Subtracting eq (i) from eq (ii)
d, or common difference = {{{matrix(1,3, (- 10)/5, "=", - 2)}}}

{{{matrix(1,3, 2a[1] + 9(- 2), "=", - 12)}}} ------ Substituting - 2 for d in eq (i)
{{{matrix(1,11, 2a[1] - 18, "=", - 12, "=====>", 
2a[1], "=", 6, "=====>",
a[1], "=", 6/2 = 3)}}}
To find {{{a[18]}}}, we substitute {{{matrix(1,10, 18, for, "n,", - 2, for, "d,", and, 3, for, a[1])}}} into the formula for a term in an A.P., as follows: {{{highlight_green(system(matrix(3,3, a[n], "=", a[1] + (n - 1)d,
a[18], "=", 3 + (18 - 1)- 2,
a[18], "=", 3 - 34),
highlight(matrix(1,3, a[18], "=", - 31))))}}}</pre>