Question

terms will amount to 60 in the series16+14+12​

Answer 1

Answer:

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Answer 2

The total number of terms(n) = 12 or, 5

Step-by-step explanation:

The given series are:

16 + 14 + 12​ + 10 + ...........

The given series are in AP.

Here, first term (a) = 16, common difference (d) = 14 - 16 = - 2

Let the number of terms = n

To find, the number of terms = ?

We know that,

The sum of up to nth term of an AP

$S_{n} =\dfrac{n}{2} [2a+(n-1)d]$

⇒ $\dfrac{n}{2} [2(16)+(n-1)(-2)]=60$

⇒ n(32 - 2n + 2) = 60 × 2 = 120

⇒ n(34 - 2n) = 120

⇒ 34n - 2$n^2$ = 120

⇒ $n^2$ - 17n + 60 = 0

⇒ $n^2$ - 12n - 5n + 60 = 0

⇒ (n - 12)(n - 5) = 0

⇒ n = 12 or, 5

Thus, the total number of terms(n) = 12 or, 5