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State True/False.

If the sum of first n term of an AP is $S n = 2 n − 3 n 2$ whose nth term is 5-6n, then the sum of its first 20 terms is -1160.

Topic Introduction to Arithmetic Progressions

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True

False

answer is A.

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Detailed Solution

Given that,

S n = 2 n − 3 n 2

.
Formula for the

n t h

term:

a n = a + n − 1 × d

Consider a n be the n th term of AP ∴ a n = 5 − 6 n

Substitute n = 1 and calculate 1 st term: ∴ a 1 = 5 − 6 × 1 ⇒ a 1 = − 1

Substitute n = 2 and calculate the 2 nd term: ∴ a 2 = 5 − (6 × 2) ⇒ a 2 = − 7

Let d be the common difference of the AP:

∴ d = a 2 − a 1 ⇒ d = − 7 − (− 1) = − 7 + 1 = − 6

Determining the sum of first 20 terms of the AP by putting the values in equation (1),

S n = 2 n − 3 n 2 [g i v e n]

∴ S 20 = 2 × 20 − 3 × 202 ⇒ S 20 = 40 − 1200 = − 1160

Therefore, the sum of the first 20 terms of the AP is -1160.
Thus, the given statement is true.
Hence, option (1) is correct.

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