Question

What is the sum of the first 4 terms of the arithmetic sequence in which the 8th term is 10 and the 14th term is 29.5?

Answer 1

Answer:

Sum of the first 4 terms is

14.50

Explanation:

In an arithmetic sequence, whose first term is

a

and difference between a term and its preceding term is

d

,

the

n

t

h

term is

a

+

(

n

−

1

)

d

and sum of first

n

terms is

n

2

(

2

a

+

(

n

−

1

)

d

)

Hence

6

t

h

term will be

a

+

5

d

=

8

and

10

t

h

term will be

a

+

9

d

=

13

Subtracting first from second,

4

d

=

5

or

d

=

1.25

and

a

=

8

−

5

⋅

1.25

=

8

−

6.25

=

1.75

Hence sum of first four terms is

4

2

⋅

(

2

⋅

1.75

+

3

⋅

1.25

)

=

2

⋅

(

3.5

+

3.75

)

=

2

⋅

7.25

=

14.50