Question

Assertion (A) : For an A.P., 3,6,9, …, 198, 10th term from the end is 168. Reason (R) : If 'a' and 'l' are the first term and last term of an A.P. with common difference 'd', then nth term from the end of the given A.P. is l − (n − 1) d.

In an equilateral triangle of side 10 cm, equilateral triangles of side 1 cm are formed as shown in the figure below, such that there is one triangle in the first row, three triangles in the second row, five triangles in the third row and so on. Based on given information, answer the following questions using Arithmetic Progression.

Cable cars at hill stations are one of the major tourist attractions. On a hill station, the length of cable car ride from base point to top most point on the hill is 5000 m. Poles are installed at equal intervals on the way to provide support to the cables on which car moves. The distance of first pole from base point is 200 m and subsequent poles are installed at equal interval of 150 m. Further, the distance of last pole from the top is 300 m. Based on above information, answer the following questions using Arithmetic Progression :

An AP consists of 'n' terms whose nᵗʰ term is 4 and the common difference is 2. If the sum of 'n' terms of AP is –14, then find 'n'. Also, find the sum of the first 20 terms.