if Sn=n^2+24 find a18
Points luto pls answer fast
Answers
Answer:
a₁₈ = 35
Step-by-step explanation:
Given---> Sₙ = n² + 24
To find ---> a₁₈ = ?
Solution--->
Sₙ = n² + 24
Putting n = 1 in it
S₁ = 1² + 24
= 1 + 24
S₁ means sum of one term which is only first term
S₁ = a₁ = 25
Now putting n= 2 in Sₙ
S₂ = ( 2 )² + 24
= 4 + 24
= 28
S₂ means sum of first two terms which are a₁ and a₂
S₂ = a₁ + a₂ = 28
25 + a₂ = 28
a₂ = 28 - 25
a₂ = 3
Now putting n = 3 in Sₙ
S₃ = 3² + 24
= 9 + 24
S₃ = 33
S₃ means sum of first three terms
a₁ + a₂ + a₃ = 33
25 + 3 + a₃ = 33
a₃ = 33 - 28
a₃ = 5
a₁ = 25 , a₂ = 3 , a₃= 5
a₂ - a₁= 3 - 25 = - 22
a₃ - a₂ = 5 - 3 = 2
a₂ - a₁ ≠ a₃ - a₂
So it is not an AP
Now
Sₙ = n² + 24
Putting n = 18 in it
S₁₈ = ( 18 )² + 24
= 324 + 24
Putting n = 17 in Sₙ
S₁₇ = ( 17 )² + 24
= 289 + 24
S₁₈ means sum of 18 terms and S₁₇ means sum of 17 terms
If we subtract S₁₇ from S₁₈ we get a₁₈
a₁₈ = S₁₈ - S₁₇
= (324 + 24 ) - ( 289 + 24 )
= 324 + 24 - 289 - 24
= 324 - 289
a₁₈ = 35
Answer:
This sequence is not an AP because in General expression of sum of n terms of an AP square of n not comes.
So,
Continuing in this way we get,
So,
18th term of the given sequence will be 35 .