Question

find sum of first 10 terms of an AP whose first term is minus 5 and third term is 5

Answer 1

Answer:

• Sum of first 10 terms = 175.

Step By Step Explanation:

Given:

• First term, a₁ = -5
• Third term, a₃ = 5

To Find:

• Sum of first 10 terms.

Now, firstly we will find common difference,

We know that,

=> a₃ = a + 2d

=> 5 = -5 + 2d

=> 10 = 2d

=> d = 10/2

=> d = 5

Hence, common difference = 5

Now, we will come calculate sum of first 10 terms.

=> Sn = n/2[2a + (n - 1)d]

=> S₁₀ = 10/2[-10 + (10 - 1)5]

=> S₁₀ = 5[-10 + 45]

=> S₁₀ = 5[35]

=> S₁₀ = 175

Hence, sum of first 10 terms = 175.

Answer 2

Answer:

Given:

• First term is -5 and third term is 5.

Find:

• Find sum of first 10 terms of an AP.

According to question:

• First term = -5.

• Third term = 5.

Know terms:

• (AP) = Arithmetical process.

• (a₁) = First term.

• (a₃) = Third term.

• (Sn) Summation notation.

• (d) = Difference.

Finding the common difference and then calculating the sum first of first 10 terms.

Finding the difference:

⇒ a₃ = a + 2d

⇒ 10 = 2d

⇒ d = 10/2 = 5d

⇒ [d = 5]

Therefore, common difference = 5.

Sum of first 10 terms:

⇒ Sn = n/2 [2a + (n - 1) d]

⇒ S₁₀ = 10/2 [- 10 + (10 - 1) 5]

⇒ S₁₀ = 5 (- 10 + 45)

⇒ S₁₀ = [5 × 35 = 175]

⇒ [S₁₀ = 175]

Therefore, 175 is the sum of first 10 terms.