QJEEM19Mac1bd: JEE Main 2019 Mathematics - Class 11 JEEM19Mac1bd Solution: Let the sum of the first n terms of a non-constant A.P., a 1 ,…

Question

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Let the sum of the first n terms of a non-constant A.P., a₁, a₂, a₃, ..... be

50 n + \frac{n (n - 7)}{2} A

, where A is a constant. If d is the common difference of this A.P., then the ordered pair (d, a₅₀) is equal to

Accepted Answer

S_n =

50 n + \frac{n (n - 7)}{2} A

We know, n^th tem

T_n = S_n - S_{n - 1}

=

50 n + \frac{n (n - 7)}{2} A

-

50 (n - 1) - \frac{(n - 1) (n - 8)}{2} A

= 50 +

\frac{A}{2} [n^{2} - 7 n - n^{2} + 9 n - 8]

= 50 + A(n - 4)

We also know, common difference

d = T_n - T_{n - 1}

= 50 + A(n - 4) - 50 - A(n - 5)

= A

And T₅₀ = 50 + A(50 - 4)

= 50 + 46A

∴

(d, a₅₀) = (A, 50+46A)

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