Question

in an a. p. 16,14,12....,the sum of how many terms is 60? why we get double answer? explain step by step. ​

Answer 1

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Answer 2

Answer:

Given:-

• A.p = 16, 14, 12 ......
• sn = 60

To find

• n = ?

Solution:-

• a = 16
• d = - 2

$s_{n} = \frac{n}{2} (2a + (n - 1) \times d) \\ \\ 60 = \frac{n}{2} \times (2 \times 16 + (n - 1) \times - 2) \\ \\ 60 = \frac{n}{2} \times (32 - 2n + 2) \\ \\ 60 = \frac{n}{2} \times (34 - 2n) \\ \\ 60 \times 2 = n(34 -2 n) \\ \\ 120 = 34n - 2{n}^{2} \\ \\ 2{n}^{2} - 34n + 120 = 0 \\ \\ divide \: this \: equation \: by \: 2 \\ \\ {n}^{2} - 17n + 60 = 0\\ now \: factorise \: this \\ \\ {n}^{2} - 12n - 5n + 60 = 0 \\ \\ take \: common \\ \\ n(n - 12) - 5(n - 12) = 0 \\ \\ (n - 12)(n - 5) = 0 \\ \\ n = 12 \: or \: n \: = 5$