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