Advertisements
Advertisements
Question
Find the sum (−5) + (−8)+ (−11) + ... + (−230) .
Advertisements
Solution
(−5) + (−8)+ (−11) + ... + (−230) .
Common difference of the A.P. (d) = a2 - a1
=-8-(-5)
=-8+5
=-3
So here,
First term (a) = −5
Last term (l) = −230
Common difference (d) = −3
So, here the first step is to find the total number of terms. Let us take the number of terms as n.
Now, as we know,
an = a + (n-1) d
So, for the last term,
- 230 = -5 + ( n-1) (-3)
- 230 = -5-3n + 3
-23 +2 = -3n
`(-228)/(-3) = n`
n = 76
Now, using the formula for the sum of n terms, we get
`S_n = 76/2 [2(-5) + (76-1) (-3)]`
= 38 [-10+(75)(-3)]
=38 (-10-225)
= 38(-235)
= -8930
Therefore, the sum of the A.P is Sn = -8930
APPEARS IN
RELATED QUESTIONS
In an AP given l = 28, S = 144, and there are total 9 terms. Find a.
Which term of the A.P. 121, 117, 113 … is its first negative term?
[Hint: Find n for an < 0]
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
Find the sum of all 3 - digit natural numbers which are divisible by 13.
Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
What is the sum of first n terms of the AP a, 3a, 5a, …..
If the sum of first p terms of an AP is 2 (ap2 + bp), find its common difference.
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
The Sum of first five multiples of 3 is ______.
In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
Sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.
The common difference of the A.P.
The common difference of the A.P. \[\frac{1}{2b}, \frac{1 - 6b}{2b}, \frac{1 - 12b}{2b}, . . .\] is
The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.
If the third term of an A.P. is 1 and 6th term is – 11, find the sum of its first 32 terms.
The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
