Arithmetic Progressions

Arithmetic Progressions

Question

Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24th term.

Answer

Given: S20 = -240  and a = 7

Consider,  S20 = -240

   Sn = n22a + (n-1) d  -240 =  2022 x 7 + (20-1) d -240 = 10 (14 + 19d) -24  = 14 + 19d   -24 - 14 = 19d  19d = -38 d= -2

Now, a24 = a + 23d

              = 7 + 23 x (-2)

              = -39

Hence, a24 = -39

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