how many terms of the A.P -6,-11/2,-5 _______ are needed to give the sum – 25? Explain the double answer​

1 thought on “how many terms of the A.P -6,-11/2,-5 _______ are needed to give the sum – 25? Explain the double answer​”

1. Answer:

   5 terms

   Step-by-step explanation:

   Given:

   a1 = -6

   d = a2-a1 = -11/2 – (-6) = 1/2

   Sn = – 25

   To find :

   number of terms needed to give the sum -25.

   we have,

   Solution:

   Sum if n terms of an A.P is given by

   Sn = n/2[2a + (n-1)d]

   [tex] – 25 = \frac{n}{2} (2( – 6) + (n – 1) \frac{1}{2} ) \\ – 25 = \frac{n}{2} ( – 12 + \frac{n – 1}{2} ) \\ – 25 = \frac{n}{2} ( \frac{ – 24 + n – 1}{2} ) \\ – 25 = \frac{n}{2} ( \frac{ – 25 + n}{2} ) \\ – 25 = \frac{ – 25n + {n}^{2} }{4} \\ – 100 = – 25n + {n}^{2} \\0 = {n}^{2} – 25n + 100 \\ 0 = {n}^{2} – 20n – 5n + 100 \\ 0 = n(n – 20) – 5(n – 20) \\ 0 = (n – 5)(n – 20) \\ therefore \\ n = 5 \: \: \: or \: \: \: \: n = 20[/tex]

   By taking 5 as the value of n we get the sum to be -25.

   Thus, 5 terms are needed to give the sum -25.

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