Question

which term of the AP 20,77/4,37/2,71/4,.........is it first negative term​

Answer 1

Answer:

28th term of the given A.P. is the first negative term.

Step-by-step explanation:

nth term of the A.P = {a + (n -1) x d}

Where, a ------> first term

            d ------> common difference

In the given A.P.,

First term (a) = 20

Common difference (d) = (2nd term - 1st term)

                                      = ($\frac{77}{4}$ - 20)

                                      = $\frac{77-80}{4}$

                                      = $\frac{-3}{4}$

To find the first negative term of the A.P.,

First, assume that nth term < 0

∴ a + (n - 1)d < 0

⇒ 20 + (n - 1)($\frac{-3}{4}$) < 0

⇒ 20 - $\frac{3n}{4}+\frac{3}{4}$ < 0

⇒$20+\frac{3}{4}-\frac{3n}{4}$ < 0

⇒$\frac{80+3}{4}-\frac{3n}{4}$ < 0

⇒$\frac{83}{4}-\frac{3n}{4}$ < 0

⇒$\frac{83}{4}<\frac{3n}{4}$

⇒ 83 < 3n

⇒ n > $\frac{83}{3}$

⇒ n > 27.66

∴ It means that the 28th term be the first negative term.

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