QJEEM20Macb6c: JEE Main 2020 Mathematics - Class 11 JEEM20Macb6c Solution: Let a 1 , a 2 , ..., an be a given A.P. whose common difference …

Question

Verified Solution • 2025–26 Session moderate

Let a₁, a₂, ..., an be a given A.P. whose
common difference is an integer and
S_n = a₁ + a₂ + .... + a_n. If a₁ = 1, a_n = 300 and 15

\leq

n

\leq

50, then
the ordered pair (S_n-4, a_n–4) is equal to:

Accepted Answer

a_{n} = a_{1} + (n - 1) d

\Rightarrow 300 = 1 + (n - 1) d

\Rightarrow (n - 1) d = 299 = 13 \times 23

since, n

\in

[15, 50]

∴

n = 24 and d = 13

a_{n - 4} = a_{20} = 1 + 19 \times 13 = 248

\Rightarrow a_{n - 4} = 248

S_{n - 4} = \frac{20}{2} {1 + 248} = 2490

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