Question

find the sum of 14 arithmetic mean between 5 and 8​

Answer 1

Let A1, A2, A3,.......A14 be the 14 AM's between 5 and 8.Now, 5, A1, A2, A3,.......A14, 8 are in AP.Let d be the common difference.Now, first term, a = 5Now, a16 = 8⇒a+15d = 8⇒5+15d = 8⇒15d = 3⇒d = 15Now, A1 = a+d = 5 + 15 = 265A2 = a+2d = 5 + 25 = 275A3 = a+3d = 5 + 35 = 285A4 = a+4d = 5 + 45 = 295A5 = a+5d = 5 + 55 = 305A6 = a+6d = 5 + 65 = 315A7 = a+7d = 5 + 75 = 325A8 = a+8d = 5 + 85 = 335A9 = a+9d = 5 + 95 = 345A10 = a+10d = 5 + 105 = 355A11 = a+11d = 5 + 115 = 365A12 = a+12d = 5 + 125 = 375A13 = a+13d = 5 + 135 = 385A14 = a+14d = 5 + 145 = 395Now, A1 + A2 + .......+A14 = 265+275 + .......395 = 4555 = 91Now, AM between 5 and 8 = 5+82 = 132Now, 14 times AM between 5 and 8 = 14 ×132 = 91So, A1 + A2 + .......+A14 = 14 times AM between 5 and 8

follow me i will follow u back