Read the text carefully and answer the questions: The students of a school decided to beautify the school on an annual day by fixing colourful flags on the s passage of the school. They have 27 flags to be fixed at intervals of every 2 metre. The flags are stored at position of the middlemost flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her bo where the flags were stored. She could carry only one flag at a time. (1) How much distance did she cover in pacing 6 flags on either side of center point? Represent above information in Arithmetic progression (ii) OR What is the maximum distance she travelled carrying a flag? (ii) How much distance did she cover in completing this job and returning to collect her books? Read the text carefully and answer the questions:
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Step-by-step explanation:
Distance travelled for fixing & coming back to A for
(i) first flag = (2+2)m = 4m = a
(ii) second flag = (4+4)m = 8m = a2
(iii) third flag = (6+6)m = 12m = a3
∴ a, a2 , a3 ... from an AP in which a = 4 , a2 = 8 , a3 = 12.... n = 13 and common difference, d = 8 - 4 = 4.
Sn = ( n /2) [ 2a = (n -1) d]
∴ S 13 = (13/2) [2 × 4 + (13 - 1)4]
= (13/2) (8+48)
= (13/2) × 56
= 364
∴ Distance travelled to fix 13 flags to the left of A = 364m
Similarly, distance travelled to fix remaining 13 flags to the right of A = 364m
∴ Total distance travelled = 2 × 364 m
= 728m
Now, the maximum distance she travelled carrying a flag = Distance travelled by Ruchi during placing the 14th flag in her left position or 27th flag in her right position
= (2 + 2 + 2 + ... + 13 times)
= 2 × 13 = 26 m
Hence, the maximum distance she travelled carrying a flag is 26 m.