pushpitkc wrote:
In a sequence of integers, each term in the first m integers is 5 greater than the previous integer. Thereafter, each integer is 2 less than the previous integer. If the first integer and the last integer in the sequence are each 50 and the number of integers in the sequence is 29, m=?
A. 7
B. 9
C. 10
D. 12
E. 15
Source:
Experts GlobalFirst, we have m integers, for which each term is 5 greater than the previous integer:
50, 55, 60, 65, 70, ..., 50 + 5(m - 1)
Notice, that the last integer in this, first, part of the sequence is \(50 + 5(m - 1)\).
\(n_{th}\) term in the arithmetic progression (AP) is given by \(a_n=a_1+d(n-1)\), where d is the common difference.
After those m integers, each integer is 2 less than the previous integer:
\([50 + 5(m - 1)] - 2\), \([50 + 5(m - 1)] - 4\), \([50 + 5(m - 1)] - 6\), ..., 50.
Notice, that since there are a total of 29 integers in the whole sequence, then the above continues for 29 - m integers. The last integer given to be 50, thus by applying the same rule for AP, we'll get \(50 = [50 + 5(m - 1) - 2] + (-2)[(29 - m) - 1]\):
\(0 = 5m - 7 -56 + 2m\)
\(7m=63\);
\(m=9\).
Answer: B.
12. Sequences
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