Math, asked by Ori123, 1 year ago

if Sn=n^2+24 find a18
Points luto pls answer fast

Answers

Answered by rishu6845
4

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

Answered by SparklingBoy
3

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,

S_n =  {n}^{2}  + 24 \\  \\ a_1 = S_1  = 1 + 24   =  25 \\  \\ a_2 =S_2 - S_1  \\ = 28 - 25 \\  = 3 \\  \\ a_3 = S_3 - S_2 \\  = 33 - 28 \\  = 5 \\ . \\.  \\ . \\ . \\ . \\ . \\ . \\ . \\

Continuing in this way we get,

a_{18} = S_{18} - S_{17} \\  =  ({18}^{2}  + 24) - ( {17}^{2}  + 24) \\  = 348 - 313 \\  = 35

So,

18th term of the given sequence will be 35 .

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