Question

If Sn=2n²-3n, Find it's 25th term. Solve step by step. I will Mark him.

Answer 1

GiveN :

• Sn = 2n² - 3n

To FinD :

• 25th term of the AP

SolutioN :

Take the equation of the Sum of n terms of AP

➠n = 1

⇒S1 = 2(1)² - 3(1)

⇒S1 = 2 - 3

⇒S1 = -1

∴ Sum of 1st term or simply 1st term of AP is -1.

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➠ Put n = 2

⇒S2 = 2(2)² - 3(2)

⇒S2 = 2(4) - 6

⇒S2 = 8 - 6

⇒S2 = 2

∴ Sum of two terms is 2

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Now, we'll find out 2nd term

⇒A2 = S2 - S1

⇒A2 = 2 - (-1)

⇒A2 = 2 + 1

⇒A2 = 3

∴ Second term of AP is 3.

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Now, we'll find common difference

⇒d = A2 - A1

⇒d = 3 -(-1)

⇒d = 3 + 1

⇒d = 4

∴ Common Difference is 4

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Now, for 25th term,

⇒A25 = a + 24d

⇒A25 = - 1 + 24(4)

⇒A25 = -1 + 96

⇒A25 = 95

$\therefore$ 25th term of AP is 95.

Answer 2

Given ,

The sum of first n terms of AP is

• Sn = 2n² - 3n

We know that ,

$\large \boxed{ \sf{a_{n} = S_{n}- S_{(n - 1)}}}$

Thus ,

$\sf \mapsto a_{25} = S_{25} - S_{24}\\ \\ \sf \mapsto a_{25} = 2 \times {(25)}^{2} - 3 \times 25 - \{2 \times {(24)}^{2} - 3 \times 24 \} \\ \\ \sf \mapsto a_{25} =2 \times 625 - 75 - 2 \times 576 - 72\\ \\ \sf \mapsto a_{25} = 1250 - 75 - 1152 + 72 \\ \\ \sf \mapsto a_{25} =95$

$\sf \therefore \underline{The \: 25th \: term \: of \: given \: AP \: will \: be \: 95}$