An arithmetic sequence has terms a3 = 11.7 and a8 = −14.6. What is the first term?

Expert Solution

Consider an arithmetic sequence with a3 = 11.7 and a8 = -14.6.

Use the formula for nth term of an arithmetic sequence,

an = a1 + (n – 1)d ...... (1)

Substitute n = 3 and a3 = 11.7 in formula (1) an = a1 + (n – 1)d and simplify,

a3 = a1 + (3 – 1)d

11.7 = a1 + 2d ...... (2)

Substitute n = 8 and a8 = -14.6 in formula (1) an = a1 + (n – 1)d and simplify,

a8 = a1 + (8 – 1)d

-14.6 = a1 + 7d ...... (3)

Subtract equation (2) from equation (3)

-14.6 = a1 + 7d

11.7 = a1 + 2d

-26.3 = 5d

Division by 5 gives,

d = -26.3/5

= -5.26

Substitute d = -5.26 in equation (2) 11.7 = a1 + 2d and solve,

11.7 = a1 + 2 × (-5.26)

11.7 = a1 – 10.52

a1 = 11.7 + 10.52

= 22.22

Therefore, first term of given sequence is a1 = 22.22.

Junaid answered 1 year ago

An arithmetic sequence has the first term a1 = 18 and common difference d = −8. What are the first five terms?

For the arithmetic progression a1, a2, a3 .......... if a4/a7 = 2/3. Find a6/a8 ?

Use the formula for the general term (the nth term) of an arithmetic sequence to find...

Use the formula for the general term (the nth term) of an arithmetic sequence to find the sixth term of the sequence with the given first term and common difference. a1 =15; d=7 a6 =

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 formula for the sum of the first n terms of each arithmetic sequence. 3.2 + 3.4 + 3.6 + … + 5.6

For the following exercises, use the formula for the sum of the first n terms of each arithmetic sequence.3.2 + 3.4 + 3.6 + … + 5.6

Use the formula for the sum of the first n terms of an arithmetic series to find the sum of the first eleven terms of the arithmetic series 2.5, 4, 5.5, … .

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

How many terms are in the finite arithmetic sequence 12, 20, 28, … , 172?

If the pth term of an arithmetic progression is c and the qth term is d, what is the value of next rth term in terms of c and d?

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

Question