Question

11). If the ratio of the 11" term of an AP to its 18** term is 2:3,find the
ratio of the sum of the first 5 terms to the sum of its first 10 terms.​

Answer 1

Answer:

6 : 17

Step-by-step explanation:

ratio of 11th term and 18th term is 2:3

$\frac{a + 10d}{a + 17d} = \frac{2}{3} \\ 3(a + 10d) = 2(a + 17d) \\ 3a + 30d = 2a + 34d \\ 3a + 30d - 2a - 34d = 0 \\ a - 4d = 0 \\ a = 4d$

ratio of sum of first 5 term and first 10 terms

$\frac{s5}{s10} = \frac{ \frac{5}{2} (2a + 4d)}{ \frac{10}{2} (2a + 9d)} \\ = \frac{ \frac{5}{2} \times 2(a + 2d) }{5(2a + 9d)} \\ = \frac{a + 2d}{2a +9d } \\ = \frac{4d + 2d}{2(4d) + 9d} \\ = \frac{6d}{17d} \\ = \frac{6}{17}$

therefore the ratio is 6:17