Question

the sum of the first two terms of an arithmetic series is 15 and the sum of the next two terms is 43. What are the first four terms of the series? Hint: you need to find the common difference using a system of equations.

Answer 1

7,8,21,22 My best guess

Answer 2

there's no common difference in that series?

Answer 3

if a1, a2 , a3 and a4 are the terms of the arihmetic series then
\[ \large a_2=a_1+d \]
\[ \large a_3=a_2+d=a_1+d+d=a_1+2d \]
\[ \large a_4=a_1+3d \]

Answer 4

u r told that
\[ \large 15=a_1+a_2=a_1+(a_1+d)=2a_1+d \]
\[ \large 43=a_3+a_4=(a_1+2d)+(a_1+3d)=2a_1+5d \]
and now u have a liner system on a1 and d.

Answer 5

thanks!

Answer 6

u r welcome.