I recently read, “Israel did not repent of its sin at the end of the 70 years of Babylonian captivity. Some of Jews did return to the Promised Land, but the majority simply settled in the Persian Empire (Iran-Iraq). So how long until God would regather the Jews and restore them back as the Nation of Israel? The solution to the mystery is found in Leviticus 26:18. “‘If after all this you will not listen to me, I will punish you for your sins seven times over.”
If Israel did not repent, the punishment promised would be multiplied by seven times. That means 70 years would become 490 years. This is the length of Daniel’s 70 weeks. Are the Babylonian captivity and Daniel’s 70 weeks related because Israel failed to repent?
No. Even though they both contain some of the same numbers, the two prophecies are not related. The Babylonian captivity was Israel’s punishment for not keeping the Sabbath for the land. According to Leviticus 25:1-7 they were supposed to let the land lie fallow for one year out of every seven. Apparently, they had neglected to do this for 490 years and finally God decided it was time to pay up. He established the duration of the Babylonian captivity as 70 years, one for each of the Sabbaths they had ignored (Jeremiah 25:11, 2 Chron. 36:21).
The 490 years of Daniels 70 weeks were not a judgment, They were a period of time set apart by God to complete the six objectives the angel listed in Daniel 9:24;
“Seventy ‘sevens’ are decreed for your people and your holy city, to finish transgression, to put an end to sin, to atone for wickedness, to bring in everlasting righteousness, to seal up vision and prophecy and to anoint the Most Holy Place.”
At the end of this 490 year period, Israel was to have completed these six things in order to be prepared for the Kingdom age. But after 483 years they rejected the Messiah, stopping the clock 7 years short of completion, and opening the door for the Church Age. After the Church is gone they will complete the remaining 7 years, known to us as Daniel’s 70th Week.
I think the study you quoted probably referred to a different matter where some people try to combine Leviticus 26 with Ezekiel 4 and the 70-year Babylonian captivity to show that May 1948 was the fulfillment of prophecy. Even though the re-birth of Israel was the fulfillment of prophecy (Ezekiel 37), this is a very complicated formula that is not widely accepted.