find 15th term of an arithmetic series is 102 and the 31st term is 160
a: find the first term and common difference
b: find the 100th term of the series.
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Solution :
(a). A15 = 102 and A31 = 160
a + 14d = 102 --> ( i ) and a + 30d = 160 --> ( ii )
a = 102 - 14d
Put it in equation (ii)
(102 - 14d) + 30 d = 160
102 + 16d = 160
16d = 58
d = 29/8
First term, a = 102 - 14 * 29/8
a = 205/4
(ii) Now, A100 = 205 /4 + 99× 29/8
A 100 = 3281 / 8
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