Advertisements
Advertisements
Question
Find the sum of first 15 multiples of 8.
Advertisements
Solution 1
The multiples of 8 are
8, 16, 24, 32, ...
These are in an A.P., having the first term as 8 and common difference as 8.
Therefore, a = 8
d = 8
S15 = ?
`S_n = n/2[2a + (n - 1)d]`
= `15/2[2(8) + (15 - 1)8]`
= `15/2[16 + 14(8)]`
= `15/2(16 + 112)`
= `(15(128))/2`
= 15 × 64
= 960
Therefore, the sum of the first 15 multiples of 8 is 960.
Solution 2
Multiples of 8 are: 8, 16, 24, 32, ..........., which form an A.P. with first term, a = 8 and common difference, d = 8
∵ Sum of nth term of A.P.
Sn = `n/2[2a + (n - 1)d]`
∴ S15 = `15/2 [2 xx 8 + (15 - 1) xx 8]`
= `15/2 [16 + 112]`
= `15/2 xx 128`
= 15 × 64
= 960
APPEARS IN
RELATED QUESTIONS
Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3
How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer
The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees, and so on till class XII. There are three sections of each class. How many trees will be planted by the students?
Which term of the A.P. 121, 117, 113, ... is its first negative term?
[Hint: Find n for an < 0]
A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50 m^3`]
If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.
Find the sum of the first 15 terms of the following sequences having nth term as yn = 9 – 5n.
Which term of AP 72, 68, 64, 60, ... is 0?
The angles of a quadrilateral are in AP whose common difference is 10°. Find the angles.
Find the sum of the first n natural numbers.
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
Choose the correct alternative answer for the following question .
First four terms of an A.P. are ....., whose first term is –2 and common difference is –2.
Choose the correct alternative answer for the following question .
What is the sum of the first 30 natural numbers ?
In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to
The common difference of the A.P. \[\frac{1}{3}, \frac{1 - 3b}{3}, \frac{1 - 6b}{3}, ...\] is ______.
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
The sum of first ten natural number is ______.
