Question

an ap consists of 37 terms of which 7 term is 13 and the last term is 108 find the 45th term of the AP

Answer 1

ans. according to figure.

Hi dear friend your answer =
A. T. Q.
7th term = 13
a+6d = 13. ( equ 1st)

57th term = 108.
a+56d = 108. (equ 2nd)

then,
a+6d = 13
a+56d = 108
(-) (-) = (-)
____________
-50d = -95
d = -95/-50
d = 19/10.
Now put the value of d in equ 1st
a+6d = 13
a+ 6(19/10) = 13
a + 114/10 =13
a = 13-114/10
a = 130-114/10
a= 16/10
a= 8/5.

45th term = a + 44d
8/5 + 44*19/10
8/5+22*19/5
8/5+418/5
8+418/5
426/5
85.2 answer
____________________________________

Answer according that u written.
7th term = 13
a+6d = 13. (equ 1st)

37th term= 108. (equ 2nd)
a+36d = 108
a+6d = 13
a+36d= 108
(-) (-) = (-)
__________
-30d = -95
d= -95/-30
d = 19/6
put the value of d in equ 1st
a+6d = 13
a+6*19/6 = 13
a+19 = 13
a = 13-19
a= -6.

45th term = a+44d
= -6+44*19/6
= -6+22*19/3
= -6+418/3
= -18+418/3
= 400/3. ans.
it will help completely.