Question

The sum upto n terms of an A. P. is 48, first term is 20 and common difference is - 4. Find the number of
terms.
[Ans.n= 3 or 8]
​

Answer 1

Given,

Sn = 48

a = 20

d = - 4

Now,

$sn = \frac{n}{2} (2a + (n - 1)d) \\ \\ 48 = \frac{n}{2} (2 \times 20 + (n - 1) \times - 4) \\ \\ 48 \times 2 = n(40 - 4n + 4) \\ \\ 96 = n(44 - 4n) \\ \\ 96 = 44n - 4 {n}^{2} \\ \\ 4 {n}^{2} - 44n + 96 = 0 \\ \\ dividing \: by \: 4 \\ \\ {n}^{2} - 11n + 24 = 0 \\ \\ {n}^{2} - 8n - 3n + 24 = 0 \\ \\ n(n - 8) - 3(n - 8) = 0 \\ \\ (n - 8)(n - 3) = 0 \\ \\ n = 8 \: \: \: \: or \: \: \: n = 3$

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