Question

find the terms of an arithmetic sequence whose sum of the reciprocal of first two consecutive term is 1/6 and common difference is 5?​

Answer 1

Step-by-step explanation:

Let first term of AP be a and common difference be d.

According to question,

$\frac{1}{a} + \frac{1}{a + d} = \frac{1}{6}$

$\frac{1}{a} + \frac{1}{a + 5} = \frac{1}{6}$

$\frac{a + 5 + a}{ {a}^{2} + 5a } = \frac{1}{6}$

${a}^{2} + 5a = 12a + 30$

${a}^{2} - 7a - 30 = 0$

${a}^{2} - 10a + 3a - 30 = 0$

$a(a - 10) + 3(a - 10) = 0$

$(a - 10)(a + 3) = 0$

$a = 10 \: \: and \: \: a = - 3$

Therefore, possible APs are

10, 15, 20, 25, ........

-3, 2, 7, 12, ......