Advertisements
Advertisements
Question
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
Solution
In the given problem, we need to find the sum of the n terms of the given A.P. 5, 2, −1, −4, −7, ...,
So, here we use the following formula for the sum of n terms of an A.P.,
`S_n = n/2 [2a + (n -1)d]`
Where; a = first term for the given A.P.
d = common difference of the given A.P.
n = number of terms
For the given A.P. (5, 2, -1, -4, -7)
Common difference of the A.P. (d) =`a_2 - a_1`
= 2 - 5
= -3
Number of terms (n) = n
First term for the given A.P. (a) = 5
So, using the formula we get,
`S_n = n/2 [2(5) + (n -1)(-3)]`
`= n/2 [10 + (-3n + 3)]`
`= n/2 [10 - 3n + 3]`
`= n/2 [13 - 3n]`
Therefore, the sum of first n terms for the given A.P. is `n/2 [13 - 3n]`
APPEARS IN
RELATED QUESTIONS
Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
What value is generated in the above situation?
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Find the sum of the odd numbers between 0 and 50.
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
In an A.P. the first term is 25, nth term is –17 and the sum of n terms is 132. Find n and the common difference.
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
Write the sum of first n odd natural numbers.
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n)..
Find:
- its first term and common difference
- sum of its first 25 terms
