Question

An arithmetic progression consists of 20 terms. The sum of the last
five terms is 355 and the last term is 79. Find the first term and
the common difference, hence find the sum of all the terms​

Answer 1

Step-by-step explanation:

T20 = a +19d = 79 ....(1)

T16 = a + 15d

T17 = a + 16d

T18 = a + 17d

T19 = a + 18d

T20 = 79

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4a + d(15+16+17+18) + 79 = 355

4a + 66d = 276

2a + 33d = 138 ....(2)

Or, 2(a+19d) - 5d = 138

2(79) - 5d = 138 ...(from 1)

158-138 = 5d

d = 4

a = 79-19d = 79-68 = 11

Now, S20 = 10[22+19(4)]

= 10*98

= 980