In arithmetic sequences, we know that they always differ by the same amount. That mean we can clearly construct them by incrementing our common differences. Let [tex] a_1=s [/tex], that means going from 1 to 5, 1 non inclusive, would give us 4 more common differences, and going from 5 to 9, 5 non inclusive, would give us 4 again. That means:
[tex] a_5=s+4d\\
a_9=s+8d [/tex]
Giving a_5 and a_9 numerical values then solving for d:
[tex] 24=s+4d\\
40=s+8d \implies\\
16=4d \implies\\
d=4 [/tex]
I subtracted the top equation from the bottom one if that isn't clear. With that, we are done.
The value of d is 4 in the arithmetic sequence.
A arithmetic sequence is defined as an arrangement of numbers which is particular order.
The formula to find the general term of an arithmetic sequence is,
aₙ = a₁ + (n-1)d
In an arithmetic sequence d represent the common difference.
Where aₙ is nth term of sequence and a₁ is first term
Given a₅=24 and a₉=40
a₁+(5-1)d = 24
a₁+4d = 24
a₁+(9-1)d = 40
a₁+ 8d = 40
Subtract the first equation in above equation
8d - 4d = 40 -24
4d = 16
Divide each sides by 4.
d = 4
Hence, common difference = 4
Learn more about arithmetic sequence here:
brainly.com/question/21961097
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