First n term of an arithmetic series iso viven bu Sn=5/2n²+7/2n determine the first term,the common difference and tenth term
To find the first term and common difference of the arithmetic series, we need to find the formula for the nth term of the series.
Given that Sn = 5/2n² + 7/2n, we can find the formula for the nth term using the formula for the sum of an arithmetic series: Sn = n/2 * (2*a1 + (n-1)*d), where a1 is the first term, d is the common difference, and n is the number of terms.
By comparing the given sum formula with the sum formula for an arithmetic series, we can determine that a1 = 7/2 and d = 5.
Therefore, the first term is 7/2 and the common difference is 5.
To find the 10th term, we can simply substitute n = 10 into the formula for the nth term of an arithmetic series:
a10 = a1 + (10-1)*d
a10 = 7/2 + 9*5
a10 = 7/2 + 45
a10 = 59/2
Therefore, the 10th term of the arithmetic series is 59/2.