Question

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

Answer 1

Answer:

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Explanation:

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Answer 2

Given:

• a = 16
• d = -2
• Sn = 60

Sn = 60

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

n ( 32 - 2n + 2 ) = 120

34n - 2n² = 120

Divide both sides by 2.

17n - n² = 60

n² - 17n + 60 = 0

n² - 12n - 5n + 60 = 0

n ( n - 12 ) - 5 ( n - 12 ) = 0

( n - 12 ) ( n - 5 )

Case 1: n = 12

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

=> 12/2 { 32 + 11 × -2 }

=> 6 { 32 - 22 }

=> 6 × 10

=> 60

Case 2: n = 5

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

=> 6/2 { 32 + 4 × -2 }

=> 3 { 32 - 8 }

=> 3 × 24

=> 72

Since, 72 ≠ 60 , Therefore n = 5 is neglected.

And Answer is n = 12

12 terms.