Question

if the sum of first n terms of an ap is 4n-n^2 what is the first term ?what is the sum of first two terms? what is second term? similarly found the 3rd, the 10th and the nth terms?

Answer 1

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Answer 2

Answer:

The first term is  3, sum of first two terms is 4, third term is -1 and tenth term is -15 and nth term is 5 - 2n

Step-by-step explanation:

Given :  

Sn = 4n − n²

First term, a = S₁ = 4(1) − (1)²  

S1 = 4 − 1  

S1 = 3

a = 3  

First term , a = 3  

 

Sum of first two terms, S2 = 4(2) − (2)²  

S2 = 8 − 4  

S2 = 4

Sum of first two terms = 4  

 

By using the formula, nth term of the A.P., an = Sn – S(n – 1)

Second term, a₂ = S₂ − S₁

a2 = 4 − 3  

a2 = 1

Second term = 1

 

Common difference, d = a₂ - a₁

d = 1 - 3  

d = - 2

 

By using the formula ,an = a + (n - 1)d

an = 3 + (n - 1) (−2)

an = 3 − 2n + 2

an = 5 − 2n………….(1)

 

On putting n = 3 in eq 1,

a₃ = 5 − 2(3)  

a3 = 5 − 6  

a3 = −1

Third term = - 1

 

On putting n = 10 in eq 1,

a₁₀ = 5 − 2(10)  

a10 = 5 − 20  

a10 = −15

Tenth term = - 15  

 

Hence, the first term is  3, sum of first two terms is 4, third term is -1 and tenth term is -15 and nth term is 5 - 2n

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