Question 1186962
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a)<br>
S(4) = (a)+(a+d)+(a+2d)+(a+3d) = 4a+(1+2+3)d = 4a+6d<br>
S(25) = (a)+(a+d)+(a+2d)+...+(a+23d)+(a+24d) = 25a+(1+2+...+23+24)d = 25a+300d<br>
S(25) is 15 times S(4):<br>
{{{25a+300d=15(4a+6d)}}}
{{{25a+300d=60a+90d}}}
{{{210d=35a}}}
{{{a=210d/35}}}
{{{a=6d}}}<br>
b) {{{t(55)=a+54d = 6d+54d = 60d = 10a}}}<br>