Question

In an AP the sum of n terms is 1/2 (5n2+3n) . Find its 40th term

Answer 1

Hi ,

Sum of n terms = Sn = ( 5n² + 3n ) /2

first term = a = S1 = ( 5 + 3 ) / 2 = 8

S2 = [ 5 × 2² + 3 × 2 ] /2 = 13

second term = a2 = S2 - S1

a2 = 13 - 8 = 5

common difference = a2 - a1

d = 5 - 8 = -3

40th term = a40 = a + 39d

= 8 + 39 ( - 3 )

= 8 - 117

= -109

Therefore ,

required 40th term = a40 = -109

I hope this helps you.

:)

Answer 2

Answer:

-109

Step-by-step explanation:

Sum of n terms = $S_n =\frac{5n^2 + 3n}{2}$

First term = a = $S_1 =\frac{5(1)^2 + 3(1)}{2}$ = 8

$S_2 =\frac{5(2)^2 + 3(2)}{2}$

$S_2 =13$

Second term = $a_2 = S_2 - S_1$

$a_2 =13-8 =5$

Common difference =$a_2 - a_1$

d = 5 - 8 = -3

Formula of nth term = a+(n-1)d

40th term = $a_{40}= a + 39d$

$a_{40}= 8 + 39 (-3)$

$a_{40}= 8 - 117$

$a_{40}= -109$

Hence the 40th term is -109