Find 15th term of an arithmetic series is 102 and the 31st term is 160

1.	Find 15th term of an arithmetic series is 102 and the 31st term is 160a: find the first term and common difference b: find the 100th term of the series.
Answer» 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

Find 15th term of an arithmetic series is 102 and the 31st term is 160a: find the first term and common difference b: find the 100th term of the series.

Answer»

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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Find 15th term of an arithmetic series is 102 and the 31st term is 160a: find the first term and common difference b: find the 100th term of the series.

SOLUTION :

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