Question

27. 120 logs are stacked keeping 15 logs in the
bottom row, 14 in the next row, 13 in the row next
to it and so on. In how many rows the 120 logs are
placed and how many logs are in the top row ?​

Answer 1

Answer:

15 rows

1 log at top

Step-by-step explanation:

15, 14, 13 ...,...

a = 15 d = -1

total number of logs = 120

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

$120 = \frac{n}{2} (2(15) + (n - 1) - 1) \\ 120 = \frac{n}{2} (30 - n + 1) \\ 120 \times 2 = n(31 - n) \\ 240 = 31n - {n}^{2} \\ {n}^{2} - 31n + 240 = 0 \\ {n}^{2} - 15n - 16n + 240 = 0 \\ n(n - 15) - 16(n - 15) = 0 \\ (n - 16)(n - 15) = 0 \\ n - 16 = 0 \: \: \: \: \: \: \: n - 15 = 0 \\ n = 16 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: n = 15$

An = a + (n-1)d

a16 = 15 + ((16-1) × -1)

= 15 + (15 × -1)

= 15 - 15

= 0

a15 = 15 + (15-1) × -1

= 15 + (14 × -1)

= 15 - 14

= 1

as there cannot be 0 logs the number of rows is 15

the top row has 1 log

hope you get your answer