Question

4 term of ap.Is 10 if 11 term of ap is 3 times of the 4 tems find the sum of 25 terms

Answer 1

hope it helps you friend

Answer 2

we are given

the 4th term of the. a.p is 10

which means

a4 = a + (n-1)d

a4=a+ (4–1)d

10= a+ 3d

this is eqn. 1

now again we are told that the 11 th term of the a.p. exceeds the three times the 4th term by 1

which means 11 th term = 3(4 th term ) + 1

we can also write it as , a+ (11–1)d = 3 (10 )+1 [ 4th term was given as 10]

now this comes out to be , a+ 10 d= 31

this is eqn.2

now we have two eqns and two variable so it can be easily solved

we subtract eqn 1 from eqn 2

we get, 7d = 31 - 10

7d = 21

d = 3

now we put this value of d in eqn, 1

we get , 10 = a + 3* 3

10 = a+ 9

this gives , a = 1

now we know both a and d so we can easily find any term of this a.p.

but we are supposed to find the sum of first 20 term of this a.p.

its formula is.

S25 =  n/2 [ 2a + (n-1) d ]

so this turns out to be , S 25 = 25/2 [ 2* 1 + ( 25- 1) 3]

S25 = 25/2 [ 2 + 24*3]

S25= 25/2 [2 + 72]

S25 = 25/2[ 74]

S25 = 25 * 37

S25 = 925