Arithmetic Series Word Problem(Easy)?

sharpie

10. The second and fifth terms of an arithmetic series are 40 and 121, respectively. Determine the sum of the first 25 terms of the series.

raj-k

Second term =40

Fifth term = 121

Let first term = A

and common difference = d

Secon term = A+d =40......(i)

and Fifth term= A+4d=121.....(ii)

Solving (i) and (ii) gives d= 27 and A=13

Sum of First n terms =(n/2){2A+(n−1)d}

Sum of First 25 terms =(25/2){2×13+(25−1)×27}=8425

barnali

For A.P series formula for nth term

is t_n = a + (n-1)d, where a is first term and d is common difference.

t_2 = 40

or, a + (2-1)d = 40

or, a + d = 40.......................(1)

t_5 = 121

or, a + (5-1)d = 121

or, a + 4d = 121..................(2)

now solving (1) and (2) we get

a = 13 and d = 27.

Formula for sum of n terms of an A.P series is

S_n = (n/2)[2a+(n-1)d]

Here, a=13, d=27, n=25

So, Sum of 25 terms is

S_25 = (25/2)[2*13+(25-1)27]

=8425

anotheropinion

8425