hadappa sabhyata ki Khoj Pramukh yogdan Dene Wale 3 ke bare mein likhen
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\huge\bold\red{➢ANSWER :-}➢ANSWER:−
➢For an A.P., let a be the first term and d be the common difference.
==>> t19 = 52, t38 = 128 …[Given]
==>>Since, tn = a + (n – 1)d
∴ t19 = a + (19 – 1)d
∴ 52 = a + 18d i.e. a + 18d = 52 …(i)
Also, t38 = a + (38 – 1)d
∴ 128 = a + 37d i.e. a + 37d = 128 …(ii)
➢ Adding equations (i) and (ii), we get
==>> a + 18d = 52
(a + 37d = 128)/(2a + 55d = 180) .....(iii)
➢ Now, Sn = n/2 [ 2a + (n - 1)d]
∴ S56 = 56/2 [ 2a + (56 - 1)d]
= 28(2a + 55d) = 28 x 180 ....[From (iii) ]
∴ S56 = 5040
∴ The sum of the first 56 terms is 5040.
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