Question

f the sum of first 13 terms of an ap is 91 and the sum of its first 30 terms is 465 find the sum of it 50 term

Answer 1

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Answer 2

Sn = n/2[a+an]

S13 = 91

S13 = 13/2[a+a+(13-1)d = 91

13[a+6d] = 91

a+6d = 7

a = 7-6d............(1)

S30 = 465

30/2[a+a+(30-1)d] = 465

15 [2a+29d] = 465

2a+29d = 31

2(7-6d)+29d = 31

14-12d+29d = 31

17d = 17

d = 1

put d = 1 in equation (1)

a = 7-6d

a = 7-6 = 1

a = 1 , d = 1

S50 = 50/2[2(1)+ (50-1)(1)]

S50 = 25[2+49]

S50 = 25×51

S50 = 1275