Question

3. समान्तर श्रेणी ज्ञात कीजिए जिसका 5वाँ पद 15 तथा तीसरे और
आठवे पदों का योग 34 है।
उत्तर:​

Answer 1

Step-by-step explanation:

Given:

$t_5=15 \: \& \: t_3 + t_8 = 34 \\ \\ \therefore \: a + (5 - 1)d = 15 \\ \\ \therefore \: a + 4d = 15 \\ \\ a = 15 - 4d.....(1)\\ \\ \because \: t_3 + t_8 = 34 \\ \\ \therefore \: a + (3 - 1)d + a + (8 - 1)d = 34\\ \\ \therefore \: a +2d + a +7d = 34\\ \\ \therefore \: 2a +9d = 34....(2) \\ \\ from \: equations \: (1) \: \& \: (2) \\ \\ 2(15 - 4d) + 9d = 34 \\ \\ \therefore \: 30 - 8d + 9d = 34 \\ \\ \therefore \: 30 + d = 34 \\ \\ \therefore \: d = 34 - 30\\ \\ \huge \red{ \boxed{\therefore \: d = 4}}\\ \\ \\ \implies \: a = 15 - 4 \times 4 = 15 - 16 = - 1 \\ \\ \implies \: \huge \blue{ \boxed {a = - 1}}$

Therefore, required AP is: - 1, 3, 7, 11,.......