Question 1162188

In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is three times the second term. Find the A. First term. B. Common difference. C. The sum of the first 100 terms
<pre>Sum of an A.P.: {{{matrix(1,3, S[n], "=", (n/2)(2a[1] + (n - 1)d))}}}
                {{{matrix(3,3, S[10], "=", (10/2)(2a[1] + (10 - 1)d), 50, "=", 5(2a[1] + 9d), 10, "=", 2a[1] + 9d)}}} ------ eq (i)

Term of an A.P.: {{{matrix(1,3, a[n], "=", a[1] + (n - 1)d)}}}
                 {{{matrix(2,3, a[2], "=", a[1] + d, a[5], "=", a[1] + 4d)}}}
Since {{{matrix(1,3, a[5], "=", 3(a[2]))}}}, we get: {{{matrix(3,3, a[1] + 4d, "=", 3(a[1] + d), a[1] + 4d, "=", 3a[1] + 3d, d, "=", 2a[1])}}}

10 = d + 9d ---- Substituting {{{matrix(1,3, d, for, 2a[1])}}} in eq (i)
10 = 10d
{{{matrix(1,7, 10/10, "=", 1, "=", d, "(common", "difference)")}}}
{{{matrix(1,6, a[1], "(", 1^(st), "term)", "=", 1/2)}}}

Sum of an A.P.: {{{matrix(1,3, S[n], "=", (n/2)(2a[1] + (n - 1)d))}}}
                {{{matrix(5,3, S[100], "=", (100/2)(2a[1] + (100 - 1)d), S[100], "=", 50(2(1/2)) + 99(1), S[100], "=", 50(1 + 99), S[100], "=", 50(100), S[100], "=", "5,000")}}}