Question

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

Answer 1

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.