if the sum of the first fifteen terms of an arithmetic sequence is 390 and the sum of the first twentyfive terms is 1025;

a) find the 8th term and 13th term

b)find the common difference of the sequence

Question

if the sum of the first fifteen terms of an arithmetic sequence
is 390 and the sum of the first twentyfive terms is 1025;
a) find the 8th term and 13th term
b)find the common difference of the sequence

Manbar Singh · Accepted Answer

Let a = first term and d = common differenceWe know that,sum of
first n terms is given by,Sn = n22a + n - 1dSo, S15 = 1522a +
14d⇒390 = 15a + 7d⇒a + 7d = 26 1S25 = 252 2a +
24d⇒ 1025 = 25 a + 12d⇒ a + 12d= 41 2Subtracting 1 from
2, we get, 5d = 15⇒ d = 3Now, from 1, we get, a + 21 =
26⇒a = 5a 8th term = a + 7d = 5 + 7 × 3 = 5 + 21 = 26
13th term = a + 12d = 5 + 12× d = 5 + 36 = 41b Common
difference, d = 3

if the sum of the first fifteen terms of an arithmetic sequence is 390 and the sum of the first twentyfive terms is 1025; a) find the 8th term and 13th term b)find the common difference of the sequence

if the sum of the first fifteen terms of an arithmetic sequence is 390 and the sum of the first twentyfive terms is 1025;

a) find the 8th term and 13th term

b)find the common difference of the sequence