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Q.1 Find the sum of following APs:

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Exercise 5.3 – Arithmetic Progressions

Question Statement

Q.1 Find the sum of the following APs:

(i) 2, 7, 12, …, to 10 terms.

Direct Answer

The sum of the first 10 terms of the given AP (2, 7, 12, …) is 245.

Solution

Given Information:

• First term (a) = 2
• Common difference (d) = 7 – 2 = 5
• Total number of terms (n) = 10
• Sum of n terms (Sn) = ?

Formula Used

To find the sum of n terms of an AP, we use the formula:

$$S_n = \frac{n}{2} [2a + (n – 1)d]$$

Step-by-Step Calculation

Step 1: Substitute the given values into the formula

$$S_{10} = \frac{10}{2} [2(2) + (10 – 1)5]$$

Step 2: Simplify the expression

$$S_{10} = 5 [4 + (9)5]$$

$$S_{10} = 5 [4 + 45]$$

$$S_{10} = 5 [49]$$

Step 3: Calculate the final value

$$S_{10} = 245$$

Final Answer

Therefore, the sum of the first 10 terms of the given AP sequence is 245.