Question

The sum of n terms of an A.p is
5n2 + 3n then sum of its 10 terms is:
PLEASE ANSWER ​

Answer 1

Given :

• Sum of n terms of an A.P = 5n² + 3n

Find out :

• Sum of 10th term

Solution :

As we know that

• Sn = n/2[2a + (n - 1)d]

→ Sn = 5n² + 3n

• If n = 1

→ S₁ = 5(1)² + 3 × 1

→ S₁ = 5 + 3 = 8

• If n = 2

→ S₂ = 5(2)² + 3 × 2

→ S₂ = 5 × 4 + 6

→ S₂ = 20 + 6 = 26

→ a₂ = S₂ - S₁

→ a₂ = 26 - 8 = 18

• If n = 3

→ S₃ = 5(3)² + 3 × 3

→ S₃ = 5 × 9 + 9

→ S₃ = 45 + 9 = 54

→ a₃ = S₃ - S₂

→ a₃ = 54 - 26 = 28

Now,

• First term (a) = 8
• Common difference(d) = a₃ - a₂ =28 - 18 =10

→ Sn = n/2[2a + (n - 1)d]

→ S₁₀ = 10/2[2*8 + (8 - 1)10]

→ S₁₀ = 5[16 + 7 × 10]

→ S₁₀ = 5[16 + 70]

→ S₁₀ = 5 × 86

→ S₁₀ = 430

Hence,

• Sum of 10th term is 430

Answer 2

Given :

• Sum of n terms of an A.P = 5n² + 3n

Find out :

• Sum of 10th term

Solution :

As we know that

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

→ Sn = 5n² + 3n

If n = 1

→ S₁ = 5(1)² + 3 × 1

→ S₁ = 5 + 3 = 8

If n = 2

→ S₂ = 5(2)² + 3 × 2

→ S₂ = 5 × 4 + 6

→ S₂ = 20 + 6 = 26

→ a₂ = S₂ - S₁

→ a₂ = 26 - 8 = 18

If n = 3

→ S₃ = 5(3)² + 3 × 3

→ S₃ = 5 × 9 + 9

→ S₃ = 45 + 9 = 54

→ a₃ = S₃ - S₂

→ a₃ = 54 - 26 = 28

Now,

First term (a) = 8

Common difference(d) = a₃ - a₂ =28 - 18 =10

→ Sn = n/2[2a + (n - 1)d]

→ S₁₀ = 10/2[2*8 + (8 - 1)10]

→ S₁₀ = 5[16 + 7 × 10]

→ S₁₀ = 5[16 + 70]

→ S₁₀ = 5 × 86

→ S₁₀ = 430

Hence,

Sum of 10th term is 430