Question

3. How many terms of the A. P. 16, 14, 12, ... are needed to give the sum 60? Explain
why we get two answers ?
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Answer 1

Sn = 60

=> n/2 { 2a + (n - 1)d } = 60

=> n/2 { 2 × 16 - 2n + 2 } = 60

=> n { 32 + 2 - 2n } = 120

=> 34n - n² = 120

=> n² - 34n + 120 = 0

=> n² - 30n - 4n + 120 = 0

=> n ( n - 30) - 4 ( n - 30 ) = 0

=> ( n - 4 ) ( n - 30 )

Answer: 5 terms