Question:
What is the sum of the following series?
\[
-64,\ -66,\ -68,\ ......,\ -100
\]
What is the sum of the following series?
\[ -64,\ -66,\ -68,\ ......,\ -100 \]
\[ -64,\ -66,\ -68,\ ......,\ -100 \]
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For A.P. sums, always find number of terms first, then apply \(S_n = \frac{n}{2}(a + l)\).
Updated On: Apr 21, 2026
- $-1458$
- $-1558$
- $-1568$
- $-1664$
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The Correct Option is B
Solution and Explanation
Concept:
This is an Arithmetic Progression (A.P.) where:
\[
a = -64,\quad d = -2,\quad l = -100
\]
Sum of A.P.:
\[
S_n = \frac{n}{2}(a + l)
\]
Step 1: Find number of terms.
\[ l = a + (n-1)d \] \[ -100 = -64 + (n-1)(-2) \] \[ -36 = (n-1)(-2) \Rightarrow n-1 = 18 \Rightarrow n = 19 \]
Step 2: Find the sum.
\[ S_n = \frac{19}{2}(-64 - 100) = \frac{19}{2}(-164) = 19 \times (-82) = -1558 \]
Hence, the sum is $-1558$.
Step 1: Find number of terms.
\[ l = a + (n-1)d \] \[ -100 = -64 + (n-1)(-2) \] \[ -36 = (n-1)(-2) \Rightarrow n-1 = 18 \Rightarrow n = 19 \]
Step 2: Find the sum.
\[ S_n = \frac{19}{2}(-64 - 100) = \frac{19}{2}(-164) = 19 \times (-82) = -1558 \]
Hence, the sum is $-1558$.
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