Each of the series 13 + 15 + 17+…. And 14 + 17 + 20+… is continued to 100 terms. Find how many terms are identical between the two series.
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Look for common pattern:
Series 1 = 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31
Series 2 = 14 + 17 + 20 + 23 + 26 + 29 + 32
⇒ every 3rd number of the series 1 is the same as the 2nd number in the series 2.
Find the common difference:
Common difference for series 1 = 2
Common difference for series 2 = 3
⇒ Series 1 has a smaller last term
Find the number of identical terms:
100 ÷ 3 = 33 remainder 1
⇒ There are 33 identical terms
Answer: There are 33 identical terms
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