Advertisements
Advertisements
Question
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
Options
-75
-125
75
125
Advertisements
Solution
The given sequence is 15, 10, 5,...
Here,
a = 15
d = –5
We know that,
\[S_n = \frac{n}{2}\left( 2a + \left( n - 1 \right)d \right)\]
\[ S_{10} = \frac{10}{2}\left( 2a + \left( 10 - 1 \right)d \right)\]
\[ = 5\left( 2\left( 15 \right) + 9\left( - 5 \right) \right)\]
\[ = 5\left( 30 - 45 \right)\]
\[ = 5\left( - 15 \right)\]
\[ = - 75\]
APPEARS IN
RELATED QUESTIONS
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
If Sn denotes the sum of first n terms of an A.P., prove that S30 = 3[S20 − S10]
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP.
Find the value of x for which the numbers (5x + 2), (4x – 1) and (x + 2) are in AP.
If (2p – 1), 7, 3p are in AP, find the value of p.
Find the first term and common difference for the A.P.
127, 135, 143, 151,...
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.
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
The common difference of the A.P. \[\frac{1}{3}, \frac{1 - 3b}{3}, \frac{1 - 6b}{3}, ...\] is ______.
A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find:
- the production in the first year.
- the production in the 10th year.
- the total production in 7 years.
Q.12
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
Find the sum of natural numbers between 1 to 140, which are divisible by 4.
Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136
Here d = 4, therefore this sequence is an A.P.
a = 4, d = 4, tn = 136, Sn = ?
tn = a + (n – 1)d
`square` = 4 + (n – 1) × 4
`square` = (n – 1) × 4
n = `square`
Now,
Sn = `"n"/2["a" + "t"_"n"]`
Sn = 17 × `square`
Sn = `square`
Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.
Find the sum of all odd numbers between 351 and 373.
