Question 1146198
{{{matrix(1,3,S[n],""="", expr(n/2)*(2a[1]+(n-1)d^""))}}} <--sum of first n terms.

The first term of an arithmetic sequence is 5.<pre>

{{{matrix(1,3,S[n],""="", expr(n/2)*(2(5)+(n-1)d^""))}}}

{{{matrix(1,3,S[n],""="", expr(n/2)*(10+(n-1)d^""))}}}

</pre>The ratio of the sum of the first four terms to the sum of the first ten terms is 8:35.<pre> 

Sum of first four terms: {{{matrix(1,3,S[4],""="", expr(4/2)*(10+(4-1)d^""))}}}
                         {{{matrix(1,3,S[4],""="", 2*(10+3d^""))}}}
                         {{{matrix(1,3,S[4],""="", 20+6d))}}}

Sum of first ten terms: {{{matrix(1,3,S[10],""="", expr(10/2)*(10+(10-1)d^""))}}}
                         {{{matrix(1,3,S[10],""="", 5*(10+9d^""))}}}
                         {{{matrix(1,3,S[10],""="", 50+45d))}}}

Their ratio 

{{{matrix(1,3,(50+45d)/(20+6d),""="",8/35))}}}


You solve that for d. Begin by cross-multiplying.

Edwin</pre>