Find the sum of the first 22 terms of the AP: 8, 3, -2, ...

Q: Find the sum of the first 22 terms of the AP: 8, 3, -2, ...

Given AP: 8, 3, -2, ... \nStep 1: Identify the first term ($a$), common difference ($d$), and number of terms ($n$).\nFirst term, $a = 8$\nCommon difference, $d = 3 - 8 = -5$\nNumber of terms, $n = 22$ \nStep 2: Recall the formula for the sum of the first $n$ terms of an AP. $Sn = \frac{n}{2} 2a + (n - 1)d$ \nStep 3: Substitute the values into the formula. $S{22} = \frac{22}{2} 2(8) + (22 - 1)(-5)$ \nStep 4: Simplify the expression inside the brackets. $S{22} = 11 16 + (21)(-5)$ $S{22} = 11 16 - 105$ $S{22} = 11 -89$ \nStep 5: Multiply to find the final sum. $S{22} = -979$ \nConclusion: The sum of the first 22 terms of the given AP is -979.

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Accepted Answer

Given AP: 8, 3, -2, ... 
Step 1: Identify the first term ($a$), common difference ($d$), and number of terms ($n$).
First term, $a = 8$
Common difference, $d = 3 - 8 = -5$
Number of terms, $n = 22$ 
Step 2: Recall the formula for the sum of the first $n$ terms of an AP. $Sn = \frac{n}{2} 2a + (n - 1)d$ 
Step 3: Substitute the values into the formula. $S{22} = \frac{22}{2} 2(8) + (22 - 1)(-5)$ 
Step 4: Simplify the expression inside the brackets. $S{22} = 11 16 + (21)(-5)$ $S{22} = 11 16 - 105$ $S{22} = 11 -89$ 
Step 5: Multiply to find the final sum. $S{22} = -979$ 
Conclusion: The sum of the first 22 terms of the given AP is -979.

CBSE · Class 10 · Mathematics · Arithmetic ProgressionsFind the sum of the first 22 terms of the AP: 8, 3, -2, ...