Question

Find the value of 2a + 3b

Answer 1

Answer: 19

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`