Question

Given the Arithmetic series A1+A2+A3+A4

Answer 1

Answer:

$S _{19} = 760$

Step-by-step explanation:

$a1 = 13 \\ a2 = 16 \\ d = a2 - a1 = 16 - 13 = 3 \\ d = 3 \\ a _{n} = l = 67$

now,

$a _{n} = a + (n - 1) \times d \\ 67 = 13 + (n - 1) \times 3 \\ 67 = 13 + 3n - 3 \\ 67 - 13 + 3 = 3n \\ 57 = 3n \\ 3n = 57 \\ \\ n = \frac{57}{3} \\ \\ n = 19$

now the sum of the numbers

$S _{n} = \frac{n}{2} (a + l) \\ \\ S _{19} = \frac{19}{2} (13 + 67) \\ \\ S _{19} = \frac{19}{2} (80) \\ \\ S _{19} = \frac{19}{2} \times 80 \\ \\ S _{19} = 19 \times 40 \\ S _{19} = 760$