Answer: -1
Step-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 terms
a is the first term.
d is the common difference
Sum of first term terms will be
S10 = 10/2{2a+(10-1)d}
S10 = 5{2a+9d} = 10a +45d
Similarly, for first five terms
S5= 5/2{2a+4d} = 5a+10d
Since the sum of the first ten terms of the sequence is four times the sum of the first five terms, we have
10a+45d=4(5a+10d)
10a +45d=20a +40d
Dividing through by 5
2a+9d = 4a +10d
2a+d=0
d = -2a
If the first term is 'a' and common difference is '-2a'
Second term will be ;
a+d i.e a+(-2a) = -a
Ratio of first term to second term will be a/-a = -1
