Question

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Here is your question
How many terms are there in an AP whose first term and 6th term are -12, and 8 respectively , and sum of all its term is 120 ??

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

12 terms

Step-by-step explanation:

As the question states,

1st term, a = -12

6th term, a₆ = 8

Also, given Sum of all terms, Sₙ = 120

Now,

   a₆ = 8

⇒ a + 5d = 8

⇒ -12 + 5d = 8 (Since, 1st term, a = -12)

⇒ 5d = 8 + 12

⇒ 5d = 20

⇒ d = 4

Now,

Sₙ = n/2{2a + (n-1)d}

⇒  120 = n/2{2a + (n-1)d} (Since, Sₙ = 120)

⇒  120 = n/2{2 × -12 + (n-1)4} (Since a = -12, d = 4)

⇒  120 × 2 = n{-24 + 4n - 4}

⇒  240 = n{-28 + 4n}

⇒  240 = -28n + 4n²

⇒ 4n² - 28n - 240 = 0

⇒ n² + 7n - 60 = 0

⇒ n² - (12 - 5)n - 60 = 0

⇒ n² - 12n + 5n - 60 = 0

⇒n(n - 12) + 5(n - 12) = 0

⇒ (n - 12)(n + 5) = 0

∴ Either n - 12 = 0 OR n + 5 = 0

∴ Either n = 12 OR n = -5

∴ n = 12 (Since, number of terms cannot be negative)

∴ There are 12 terms in the A.P.