Theory question 104
Sequences and SeriesThe first term of an Arithmetic Progression is −8, the last term is 52 and the sum of terms is 286. Find the: (a) number of terms in the series; (b) common difference.
Show the model answer
Model answer
(a) S = n(a + l)/2: 286 = n(−8 + 52)/2 = 22n, so n = 13.
(b) l = a + (n − 1)d: 52 = −8 + 12d, so d = 5.
Explanation
Use S = n(a + l)/2 when the first and last terms are known.