Question 1069817
{{{a[1]}}}= the first term,
{{{d}}}= the common difference, and
{{{a[2]=a[1]+d}}}= the second term.
The sum of the first 5 terms is
{{{5a[1]+10d}}} .
The sum of the first 10 terms is
{{{10a[1]+45d}}} .
The problem says that
{{{10a[1]+45d=4(5a[1]+10d)}}}
{{{10a[1]+45d=20a[1]+40d}}}
{{{45d-40d=20a[1]-10a[1]}}}
{{{5d=10a[1]}}}
{{{d=10a[1]/5}}}
{{{d÷2a[1]}}}
The ratio of the first term to the second term is
{{{a[1]/a[2]}}}={{{a[1]/(a[1]+d)}}}={{{a[1]/(a[1]+2a[1])}}}={{{a[1]/3a[1]}}}={{{highlight(1/3)}}} .