63.3k views
1 vote
1. Give the arithmetic sequence of 5 terms if the first term is 8 and the last term is 100.

2. Find the 9th term of the arithmetic sequence with a_1 = 10 and d = 1/2

3. Find a_1, if a_8 = 54 and a_9 = 60​

User Bayda
by
7.7k points

1 Answer

4 votes


{ \qquad\qquad\huge\underline{{\sf Answer}}}

Here we go ~

Problem 1 :

First term (
{ \sf a_1})= 8

Number of terms (n) : 5

Last term (
{ \sf a_((last)) }) = 100

Now, the last term can be represented as :


\qquad \sf  \dashrightarrow \: a_((last)) = a_1 + (n - 1)d

[ n = 5, as it has 5 terms and d is common difference ]


\qquad \sf  \dashrightarrow \: 100 = 8 + (5- 1)d


\qquad \sf  \dashrightarrow \: 100 = 8 + 4d


\qquad \sf  \dashrightarrow \: 4d = 100 - 8


\qquad \sf  \dashrightarrow \: d = 92 / 4


\qquad \sf  \dashrightarrow \: d = 23

So, the terms of the sequence differ by 23

Therefore, the required sequence is :

  • 8, (8 + 23), (8 + 23 + 23), (8 +23 + 23 + 23), 100

  • 8, 31, 54, 77, 100

Peoblem 2 :

First term (
{ \sf a_1}) : 10

Common difference (d) : 1/2

9th term (
{ \sf a_((9))}) = ??

The general formula for a nth term in an Arithmetic sequence is :


\qquad \sf  \dashrightarrow \: \sf a_n = a_1 + (n - 1)d

[ n = 9, as we have to find 9th term of sequence ]


\qquad \sf  \dashrightarrow \: \sf a_((9)) = 10 + (9 - 1) \sdot (1)/(2)


\qquad \sf  \dashrightarrow \: \sf a_((9)) = 10 + (8) \sdot (1)/(2)


\qquad \sf  \dashrightarrow \: \sf a_((9)) = 10 + 4


\qquad \sf  \dashrightarrow \: \sf a_((9)) = 14

So, the 9th term of the sequence is 14

Problem 3 :

The 8th term and 9th term differ by : 60 - 54 = 6

so, the common difference (d) = 6

8th term can be represented as :


\qquad \sf  \dashrightarrow \: \sf a_((8))= a_1 + (8 - 1)d


\qquad \sf  \dashrightarrow \: \sf a_((8))= a_1 + 7d

Let plug the value of 8th term, and common difference ~


\qquad \sf  \dashrightarrow \: \sf a_1 + 7(6)= 54


\qquad \sf  \dashrightarrow \: \sf a_1 + 42= 54


\qquad \sf  \dashrightarrow \: \sf a_1= 54 - 42


\qquad \sf  \dashrightarrow \: \sf a_1= 12

Hence, 1st Term of the sequence is 12

User Jean Monet
by
7.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories