Question

The sum of first 7 terms of an arithmetic sequence is 105 and the sum of first 15 terms is 465 . a ) What is its 4 th term ? b) What is its 8 th term ? c) What is its common difference ?

Answer 1

Answer:

a.) 4th term is 15

b.) 8th term is 31

c.) common difference is 4.

Step-by-step explanation:

Given :

Sum of first 7 terms, S7 = 105

Sum of first 15 terms, S15 = 465

Solution :

a.) The sum of first n terms of an arithmetic sequence is given as,

Sn = na + [(n-1)×n×d]/2.

where,

a is the first term of the sequence, and

d is the common difference of the sequence.

Thus, S7 = 7a + 21d = 105

7(a + 3d) = 105

a + 3d = 15

Here a + 3d is the 4th term of the sequence.

b.)

Now for S15 = 15a + 105d = 465

15(a + 7d) = 465

a + 7d = 31

Here a + 7d is the 8th term of the sequence.

c.) Now,

(a + 7d) - (a + 3d) = 31 - 15

4d = 16

d = 16/4 = 4

Therefore, The common difference for the sequence is 4.