Question

If the 5th term of an ap is 31 and 25th term is 140 more than 5th mm find the ap

Answer 1

Hi mate here is the answer:-

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Question:-

If the 5th term of an A.P. is 31 and 25th term is 140 more than the 5th term, find the A.P.

Answer:-

a5= 31

a+4d = 31 ..........(1)

= 140 + a5

a + 24d= 140 + 31

31 -4d +24d=171 [ from (i) ]

20d=140

d=7

Putting the value of d in (i)

a= 31 – 4(7)

= 3a1 = a=3a2 =a +d=3 +7=10a

=a +2d=3 + 2(7)

=17

Hence, the A.P. is 3, 10, 17,…

Hope it helps you ❣️❣️

Answer 2

By Question,

${t}_{5} = 31$

a + 4d = 31 -------(1)

Again,

${t}_{25} = 140 + {t}_{5}$

a + 24d = 140 + 31

a + 24d - (a + 4d) = 171 - 31

a + 24d - a - 4d = 140

20d = 140

d = 7

Now, Putting the value of d in eq (1)

a + 4d = 31

a + 28 = 31

a = 3

A.P

= a, a+d, a+2d,..........

= 3,10,17.........