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
If the mth term of an A.P. is 1/n and the nth term is 1/m, show that the sum of mn terms is (mn + 1)
Find the sum 2 + 4 + 6 ... + 200
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.
Is 184 a term of the AP 3, 7, 11, 15, ….?
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
How many two-digits numbers are divisible by 3?
Write the next term for the AP` sqrt( 8), sqrt(18), sqrt(32),.........`
If the sum of first n terms is (3n2 + 5n), find its common difference.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
Sum of 1 to n natural numbers is 36, then find the value of n.
There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
Mark the correct alternative in each of the following:
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
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`.
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
If the first term of an A.P. is 5, the last term is 15 and the sum of first n terms is 30, then find the value of n.
