seven term of ap is 32 and 13 term is 62 find nth term
Answers
Question:
Seven term of ap is 32 and 13 term is 62 find nth term ?
Answer :
an = a+ (n-1)d
Now, a7= a+6d = 32---------------(1)
a13= a+ 12d =62-------------------(2)
Subtracting (1) and (2)
-6d = (-30)
d = 5
Putting the value of 'd ' in (1)
a + 6 (5) = 32
a + 30 = 32
a = 32- 30
a = 2, d = 5
So, the required A.P is 2, 7, 12, 17,22.......
Hope it helps you !!
Answer:
Given,
7
th term of A.P
a
7
32
and 13th term of A.P is
a
13
= 62
nth term of A.P is given by
a
n
a
1
(n− 1)d
hence 7th term is given by
a
7
a
1
(7− 1)d
put
a
7
32 which is given
32=
a
1
6d...….eq(1)
13th term is given by
a
13
=
a
1
(13− 1)d
put a
13
= 62 which is given
62=
a
1
12d...….eq(2)
substract eq(1) from eq(2) we get
62− 32=
a
1
a
1
12d− 6d
⟹ 30= 6d
⟹ d=
6
30
⟹ d= 5.....eq(3) common difference
put d= 5 in eq(1) we get
32=
a
1
6× 5
⟹
a
1
32− 30
⟹
a
1
2 first term of A.P
2 nd term of A.P
a
2
a
1
d=
2+
5=
7
3 rd term of A.P
a
3
a
2
d=
7+
5=
12
4 th term of A.P
a
4
a
1
d=
12+
5=
17