In an arithmetic series, the 6th term is 39 In the same arithmetic series, the 19th term is 7.8 Work out the sum of the first 25

Question

3 years ago

5

terms of the arithmetic series.

1 answer:

Lisa [10] · Answer 1 · 2022-03-27T21:29:31+03:00

Answer:

1,500

Step-by-step explanation:

a + 5d = 39 (1)

a + 18d = 78 (2)

Subtract (1) from (2) to eliminate a

18d - 5d = 78 - 39

13d = 39

d = 39/13

d = 3

Substitute d = 3 into (1)

a + 5d = 39 (1)

a + 5(3) = 39

a + 15 = 39

a = 39 - 15

a = 24

Sum of the first 25 terms

Sn = n/2[2a + (n – 1)d]

S25 = 25/2{2*24 + (25-1)3}

= 12.5{48 + (24)3}

= 12.5{48 + 72)

= 600 + 900

= 1,500

S25 = 1,500