Find the sum of first 19th terms of an AP whose 8th term is 41 and 13th term is 61 - Maths - Arithmetic Progressions

Question

Find the sum of first 19th terms of an AP whose 8th term is 41 and
13th term is 61

Varun.Rawat · Accepted Answer

Let a be the first term and d be the common difference
Now, a8 = 41⇒a + 7d = 41     
1a13 = 61⇒a + 12d = 61    
2Subtracting 1 from 2, we get   12d - 7d = 61 - 41⇒5d = 20⇒d = 4Now, from 1, we geta + 7d = 41⇒a + 7×4 = 41⇒a + 28 = 41⇒a = 41 - 28 = 13Now, sum of first n terms of an AP is :      Sn = n22a+n-1d⇒S19 = 1922×13+18×4 = 192×98 = 931

Find the sum of first 19th terms of an AP whose 8th term is 41 and 13th term is 61.