in a certain sequence the differene between any two consecutive terms is 5.

Question

if the 20th term is 63, what is the 2nd term'?

Answer 1

20^th term of a sequence is 63 .

In the sequence difference between any two consecutive terms is 5.

In an arithmetic sequence the difference between one term and the next is a constant.

So the given sequence is arithemetic series.

Arithemetic sequence form a , a + d , a + 2d , .......,a + (n - 1)d .

In arithmetic sequence n ^th term is [a + (n - 1)d ]

Where a = first term and d  is common difference.

difference between any two consecutive terms is 5.

(a + d )  - a = 5

a + d - a = 5

d = 5

d  = 5

• To find the value of a.

20^th term = a + (20 - 1)d

Therefore a + 19d = 63

Substitute d = -5 in above equation.

a + 19(5) = 63

a - 95 = 63

a = - 95 + 63

a = -32

So the first term is a = -32

• Now the second term is a + d

2^nd term =  - 32 + 5 = - 27

Second term is - 27.