Question

An ap contains 43 terms the sun of 5 middle terms is equal to 195, find sum of the ap

Answer 1

Answer:

$five \: \: middle \: \: term \: = > \\ \\ 20th \: \: 21th \: \: 22th \: \: 23th \: \: 24th \\ \\ sum = a + 19d + a + 20d + a + 21d + a + 22d + a + 23d \\ \\ = 5a + 105d = 195 \\ \\ = > a + 21d = 39 \: \: \: \: \: \: \: \: \: ...........(1)\\ \\ sum \: \: of \: \: all \: \: term = \frac{43}{2} (2a + 42d) \\ \\ =43(a + 21d) \\ \\ = 43 \times 39 (using \: \: eq. \: \: (1) \: \: ) \\ \\ = 1677$