Question

obtain the sum of the 56 terms of an A.P whose 19th and 38th terms are 52 and 148 respectively​

Answer 1

Let  a and d be the first term and the common difference of the given AP respectively. Then,

a19=52⇒a+18d=52                    ...(1)

a38=148⇒a+37d=148                ...(2)

On subtracting (1) from (2), we get

19d=96⇒d=1996

Putting d=1996 in (1), we get

a=52−18×1996=19−740

Now, S56=256[2a+(56−1)d]

∴S56=28[193800]=5600

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