Advertisements
Advertisements
Question
A ladder has rungs 25 cm apart. (See figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 `1/2` m apart, what is the length of the wood required for the rungs?
[Hint: number of rungs = `250/25+ 1`]
Advertisements
Solution
It is given that the rungs are 25 cm apart and the top and bottom rungs are `2 1/2` m
Now, as the lengths of the rungs decrease uniformly, they will be in an A.P.
The length of the wood required for the rungs equals the sum of all the terms of this A.P.
First term, a = 45
Last term, l = 25
n = 11
Sn =` n/2(a+l)`
∴ S10 = `11/2(45+25`)
= `11/2 (70)`
= 385 cm
Therefore, the length of the wood required for the rungs is 385 cm.
APPEARS IN
RELATED QUESTIONS
If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.
The sum of the first p, q, r terms of an A.P. are a, b, c respectively. Show that `\frac { a }{ p } (q – r) + \frac { b }{ q } (r – p) + \frac { c }{ r } (p – q) = 0`
Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the nth week, her week, her weekly savings become Rs 20.75, find n.
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.
Find the sum of the first n natural numbers.
Write an A.P. whose first term is a and common difference is d in the following.
Write an A.P. whose first term is a and common difference is d in the following.
a = –1.25, d = 3
For an given A.P., t7 = 4, d = −4, then a = ______.
Choose the correct alternative answer for the following question .
If for any A.P. d = 5 then t18 – t13 = ....
The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.
Write the sum of first n odd natural numbers.
Q.7
Q.14
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
If a = 6 and d = 10, then find S10.
If ₹ 3900 will have to be repaid in 12 monthly instalments such that each instalment being more than the preceding one by ₹ 10, then find the amount of the first and last instalment.
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
Find the sum of first seven numbers which are multiples of 2 as well as of 9.
