The first and last term of an AP are 6.7 and 17.1 respectively. If there are 14 terms in the sequence,find its common difference
Let the common difference be d.
The formula for the nth term in an arithmetic sequence is given by:
an = a1 + (n-1)d
where,
an is the nth term,
a1 is the first term,
d is the common difference.
Given:
a1 = 6.7,
an = 17.1,
n = 14.
Using the formula, we can write:
17.1 = 6.7 + (14-1)d
Simplifying this equation, we have:
17.1 = 6.7 + 13d
Subtracting 6.7 from both sides, we get:
17.1 - 6.7 = 13d
10.4 = 13d
Dividing both sides by 13, we find:
d = 10.4/13
Therefore, the common difference of the arithmetic sequence is d = 0.8.
To find the common difference (d) of an arithmetic progression (AP), we can use the formula:
d = (last term - first term) / (number of terms - 1)
Given that the first term (a₁) is 6.7, the last term (aₙ) is 17.1, and the number of terms (n) is 14, we can substitute these values into the formula:
d = (17.1 - 6.7) / (14 - 1)
Simplifying this:
d = 10.4 / 13
Finally, dividing:
d ≈ 0.8
Therefore, the common difference of the arithmetic progression is approximately 0.8.
To find the common difference of an arithmetic progression (AP), we can use the formula:
common difference (d) = (last term - first term) / (number of terms - 1)
Given that the first term (a₁) is 6.7, the last term (aₙ) is 17.1, and the number of terms (n) is 14, we can substitute these values into the formula:
d = (17.1 - 6.7) / (14 - 1)
Simplifying this expression gives:
d = 10.4 / 13
Therefore, the common difference (d) of the arithmetic progression is approximately 0.8.