How to find the first term, the common difference, and the nth term of the arithmetic sequence here? 8th term is 4; 18th term is -96

3 Answers
Jul 6, 2018

First term is 74 , common difference is -10
n th term of A.P. series is T_n= a +(n-1)d

Explanation:

Let a, d ,n be the first term , common difference and number of

terms of an A.P. series

n th term of A.P. series is T_n= a +(n-1)d

8 th term of A.P. series is T_8= a +(8-1)d=4 or

a + 7 d=4 ; (1)

18 th term of A.P. series is T_18= a +(18-1)d=-96 or

a + 17 d=-96 ; (2) , subtracting equation (1) from equation (2)

we get , 10 d= -100 or d = -10 putting d=-10 in

equation (1) we get, a - 70 =4 or a = 74

Hence first term is 74 and common difference is -10 [Ans]

Jul 6, 2018

The first term is 74 and common difference is -10

Explanation:

If a Arithmatic Sequence has first term a and the common difference d then the formula of n^(th) term is
a_n=a+(n-1)d ......(1)

According to question
8^(th) term is 4
Put n=8 in equation (1)
=> a_8=a+(8-1)d=a+7d
but a_8=4
Hence =>a+7d=4 ........(2) => a=4-7d
and
18^(th) term is -96
Put n=18 in equation (1)
=> a_18=a+(18-1)d=a+17d
but a_18=-96
Hence =>a+17d=-96 ........(3)
by putting value of a from equation (2) in the equation (3)
=>(4-7d)+17d=-96
=>4+10d=-96
Transfer 4 to the Right Hand Side
=>10d=-96-4=-100
Divide by 10
(10d)/10=-100/10
d=-10

Put the value of d in equation (2) to get the first term of the Arithmetic sequence
By Equation (2)
a=4-7d=4-7(-10)
a=4+70
a=74

Hence the first term is 74 and common difference is -10

Common difference: d=-10
first term: a=74
nth term: T_n=74-10d

Explanation:

8th term
T_8=4

18th term
T_18=-96

General formula for nth tern

T_n=a+(n-1)d

(n,T_n)=(8,4)->
4=a+(8-1)xxd
Simplifying
a+7d=4-----(1)

(n,T_n)=(18,-96)->
-96=a+(18-1)xxd
Simplifying
a+17d=-96---(2)

Subtrtacting (1) from (2)
10d=-100

d=-10
Substituting
d=-10
in (1)
a+7xx(-10)=4
a-70=4
a=74

T_n=74-10d