Question

Find the sum of the first 25 terms of the sequence 1, 7, 13, 19, ....

Answer 1

Explanation:

The given series:

7

,

19

,

31

,

43

,

...

Above series is an arithmetic progression with a common difference

d

=

19

−

7

=

31

−

19

=

43

−

31

=

...

=

12

First term:

a

=

7

The sum of first

n

terms of an AP with term

a

& a common difference

d

is given as

S

n

=

n

2

(

2

a

+

(

n

−

1

)

d

)

Hence, the sum of first

n

=

25

terms of an AP with term

a

=

7

& a common difference

d

=

12

is given as

S

25

=

25

2

(

2

⋅

7

+

(

25

−

1

)

12

)

=

3775