Question

In an AP, Sn=3n/2+5n/2. Find its 25th term.

Answer 1

Sn = 3n2 + 5n
Let the number of terms be one ,
sum = 3 (1)(1) + 5 (1)
= 3 + 5
S1 = a = 8
Let the number of terms be 25,
n = 25
S25 = 3 (25)2 + 5 (25)
= 1875 - 125
S25 = 1750
Also,
S25 = 25/2 (2 * 8 + (25 - 1)d)
From above the value of S25,
1750*2 = 25 (16 + 24d)
16 + 24d = 140
24d = 124
d = 31/4
a25 = a + (25 - 1) d
= 8 + 24 * 31/4
= 8 + 186
a25 = 194

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Answer 2

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