Question

In a A.P the sum of first n term is 5n sq/2+3n/2 find the17th term

Answer 1

Answer:

17th term is 94

Step-by-step explanation:

$sum \: of \: terms \: in \: ap \\ \frac{5 {n}^{2} }{2} + \frac{3n}{2} \\ s1 = \frac{5 ({1})^{2} }{2} + \frac{3(1)}{2} = \frac{5 + 3}{2} = \frac{8}{2} = 4 \\ a1 = 4 \\ s2 = \frac{5( {2}^{2} )}{2} + \frac{3(2)}{2} = \frac{20}{2} + \frac{6}{2} = 10 + 3 = 13 \\ a2 = s2 - s1 = 13- 4 = 9 \\ s3 = \frac{5( {3}^{2} )}{2} + \frac{3(3)}{2} = \frac{45 + 9}{2} = 27 \\ a3 = s3 - s2 = 27 - 13 = 14 \\ therefore \: the \: ap \: is \\ 4 \: \: \: 9 \: \: \: 14 \: ......... \\ d = a2 - a1 = 9 - 4 = 5 \\ \\ 17th \: term \: a + 16d \\ 4 + 16(5) = 4 + 90 = 94$