Question

In: Advanced Math

For the following exercises, find the specified term given two terms from an arithmetic sequence. a1 = 33 and a7 = −15. Find a4 .

For the following exercises, find the specified term given two terms from an arithmetic sequence. 

a1 = 33 and a7 = −15. Find a4 .

Solutions

Expert Solution

Consider an arithmetic sequence with a1 = 33 and a7 = -15

Use the formula for nth term of an arithmetic sequence,

an = a1 + (n – 1)d ...... (1)

 

Substitute a1 = 33, n = 7 and a7 = -15 in formula (1),

-15 = 33 + (7 – 1)d

-15 = 33 + 6d

 6d = -15-33

 6d = 48

 

Division by 6 gives,

d = -48/6

d = -8

 

Compute forth term a4 of given sequence, substitute a1 = 33 and d = -8 in equation (1),

a4 = 33 + (4 – 1) × (-8)

     = 33 + 3 × (-8)

     = 33 – 24

     = 9

 

Therefore, fourth term of given arithmetic sequence is a4 = 9.

Therefore, fourth term of given arithmetic sequence is a4 = 9.

Junaid answered 1 year ago
Next > < Previous

Related Solutions

For the arithmetic progression a1, a2, a3 .......... if a4/a7 = 2/3. Find a6/a8 ?
For the arithmetic progression a1, a2, a3 .......... if a4/a7 = 2/3. Find a6/a8 ?
For the following exercises, find the specified term for the geometric sequence, given the first four terms. an = {−1, 2, −4, 8, ...}. Find a12.
For the following exercises, find the specified term for the geometric sequence, given the first four terms. an = {−1, 2, −4, 8, ...}. Find a12.
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence. a1 = 39; an = an − 1 −3
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence. a1 = 39; an = an − 1 −3
For the following exercises, find the common difference for the arithmetic sequence provided.
For the following exercises, find the common difference for the arithmetic sequence provided.
For the following exercises, write the first five terms of the geometric sequence, given the first term and common ratio. a1 = 5, r = 1/5
For the following exercises, write the first five terms of the geometric sequence, given the first term and common ratio. a1 = 5, r = 1/5
Find an arithmetic code for a symbol p4p4p3 for the source alphabet {a1, a2, a3, a4,...
Find an arithmetic code for a symbol p4p4p3 for the source alphabet {a1, a2, a3, a4, a5}, with symbol probabilities p1 = 0.11, p2 = 0.05, p3 = 0.10, p4 = 0.70, and p5 = 0.04. Show the work please.
5. Find the sum of terms in given arithmetic sequence 1 + 3 + 5 +...
5. Find the sum of terms in given arithmetic sequence 1 + 3 + 5 + ... + 59 6. Find the sum of terms in given arithmetic sequence 2 + 5 + 8 + ... + 41 7.Given a geometric sequence 6 + 2 + 2/3 + ... is this sequence converging or diverging, if it is converging find it's sum
For the following exercises, write a recursive formula for each arithmetic sequence. a = {−15, −7, 1, ... }
For the following exercises, write a recursive formula for each arithmetic sequence.a = {−15, −7, 1, ... }
An arithmetic sequence has the first term a1 = 18 and common difference d = −8. What are the first five terms?
An arithmetic sequence has the first term a1 = 18 and common difference d = −8. What are the first five terms?
For the following exercises, write the first five terms of the arithmetic series given two terms. a13 = −60, a33 = −160
For the following exercises, write the first five terms of the arithmetic series given two terms.a13 = −60, a33 = −160
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT