Question

Find the value of 2a + 3b

Answer 1

Answer: 19

Step-by-step explanation:

Using the sum of an arithmetic series formula,

$\sum^{30}_{n=2} (an+b)=2407 \implies 29(16a+b)=2407 \implies 16a+b=83\\\\\sum^{40}_{n=1} (an+b)=4220 \implies 20(41a+2b)=4220 \implies 41a+2b=211$

Multiplying the second equation by 2 gives us $32a+2b=166$.

Subtracting this from the second equation, we get that $9a=45 \implies a=5$.

Substituting this back into the first equation, we get that $b=3$.

Therefore, $2a+3b=2(5)+3(3)=19$