1 + (-2) + (-5) + (-8) + ... + (-236): find the sum
Solution:
Given, the series is 1 + (-2) + (-5) + (-8) + ... + (-236)
We have to find the sum of the series.
From the given series,
First term, a= 1
Last term, n = -236
Common difference, d = -2 - 1 = -3
The nth term of the series in AP is given by
aₙ = a + (n - 1)d
-236 = 1 + (n - 1)(-3)
-236 - 1 = (n - 1)(-3)
n - 1 = 237/3
n - 1 = 79
n = 79 + 1
n = 80
We know that, if l is the last term of an AP, then the sum of the terms is given by
S = n/2[a+l]
So, S = 80/2[1 + (-236)]
= 40[-235]
= -9400
Therefore, the sum of the term is -9400.
✦ Try This: Find the sum: 1 + 3 + 5 + 7+ ……………… + 27
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 21 (i)
1 + (-2) + (-5) + (-8) + ... + (-236): find the sum
Summary:
The sum of the series 1 + (-2) + (-5) + (-8) + ... + (-236) is -9400.
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