for an AP. Sn =n²+1, find a1, a2, a3 and d
Answers
Answer :
- a₁ = 1
- a₂ = 3
- a₃ = 5
- d = 2
Step-by-step explanation :
- It is the sequence of numbers such that the difference between any two successive numbers is constant.
- In AP,
a - first term
d - common difference
n - number of terms
l - last term
aₙ - nth term
Sₙ - sum of n terms
- General form of AP,
a , a+d , a+2d , a+3d , ..........
- nth term of AP,
- Sum of n terms,
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Sum of n terms = n² + 1
Let's find the sum of (n - 1) terms.
Put n = n - 1,
Sum of (n - 1) terms = (n - 1)² + 1
= n² + 1² - 2(n)(1) + 1
= n² + 1 - 2n + 1
= n² - 2n + 2
nth term = Sum of n terms - (sum of (n - 1) terms)
= n² + 1 - ( n² - 2n + 2 )
= n² + 1 - n² + 2n - 2
= 2n - 1
Therefore,
nth term , aₙ = 2n - 1
First term,
Put n = 1,
a₁ = 2(1) - 1
= 2 - 1
= 1
Second term,
Put n = 2,
a₂ = 2(2) - 1
= 4 - 1
= 3
Third term,
Put n = 3,
a₃ = 2(3) - 1
= 6 - 1
= 5
Common difference,
d = a₂ - a₁
= 3 - 1
= 2
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