The sum of the first ten terms of a particular arithmetic sequence is four times the sum of the first five terms of the sequence. What is the ratio of the first term to the second term? Express your answer as a common fraction.

Answer: -1Step-by-step explanation:A progression or sequence is an arrangement of numbers in a definite pattern. Formula for calculating sum of arithmetic sequence is given by;Sn = n/2{2a+(n-1)d}n is the number of termsa is the first term.d is the common differenceSum of first term terms will beS10 = 10/2{2a+(10-1)d}S10 = 5{2a+9d} = 10a +45dSimilarly, for first five termsS5= 5/2{2a+4d} = 5a+10dSince the sum of the first ten terms of the sequence is four times the sum of the first five terms, we have10a+45d=4(5a+10d)10a +45d=20a +40dDividing through by 52a+9d = 4a +10d2a+d=0d = -2a If the first term is 'a' and common difference is '-2a'Second term will be ;a+d i.e a+(-2a) = -aRatio of first term to second term will be a/-a = -1