An arithmetic progression consists of 37 terms. the sum of the first 3 terms of it is 12 and the sum of it's last 3 terms is 318, then find the first and last terms of the progreesion
Answers
Answer:
Given :-
In AP consists of 37 terms. The sum of first 3 terms is 12 and the sum of last 3 terms is 318
To find :-
1st and last term of AP
Solution :-
Here the first 3 terms are
a
a + d
a + 2d
\sf \implies a + a + d + a + 2d = 12⟹a+a+d+a+2d=12
\sf \implies 3a + d+ 2d = 12⟹3a+d+2d=12
\sf \implies 3a + 3d =12⟹3a+3d=12
Taking 3 as common
\sf \implies 3(a + d) = 12⟹3(a+d)=12
\sf \implies a + d = \dfrac{12}{3}⟹a+d=
3
12
\sf \implies a + d = 4⟹a+d=4
\sf \implies a = 4 - d⟹a=4−d
Now
nth term = (aₙ) = a + (n - 1)d
\sf \implies a + 36d + a + 35d + a + 34d = 318⟹a+36d+a+35d+a+34d=318
\sf \implies 3(4 - d) + 105d = 318⟹3(4−d)+105d=318
⟹ 12 - 3d + 105d = 318
⟹ 105d - 3d = 318 - 12
⟹ 102d = 318 -12
⟹ 102d = 306
⟹ d = 306/102
⟹ d = 3
⟹a = 4 - 3
⟹ a = 1
Now
⟹ a₃₇ = a + 36d
Putting d as 3
⟹ a₃₇ = 1 + 36(3)
⟹ a₃₇ = 1 + 108 = 109
i hope it's helpful to u. ❤
Given :-
In AP consists of 37 terms. The sum of first 3 terms is 12 and the sum of last 3 terms is 318
To find :-
1st and last term of AP
Solution :-
Here the first 3 terms are,
a
a + d
a + 2d
12⟹a+a+d+a+2d=12
⟹3a+d+2d=12
⟹3a+3d=12
Taking 3 as common,
⟹3(a+d)=12
⟹a+d=12/3
⟹a+d=4
⟹a=4−d
Now,
= (aₙ) = a + (n - 1)d 318⟹a+36d+a+35d+a+34d=318
3(4 - d) + 105d = 318⟹3(4−d)+105d=318
⟹ 12 - 3d + 105d = 318
⟹ 105d - 3d = 318 - 12
⟹ 102d = 318 -12
⟹ 102d = 306
⟹ d = 306/102
⟹ d = 3
⟹a = 4 - 3
⟹ a = 1
Now,
⟹ a₃₇ = a + 36d
Putting d as 3,
⟹ a₃₇ = 1 + 36(3)
⟹ a₃₇ = 1 + 108 = 109
- I Hope it's Helpful My Friend.