Question

How do you find the expression for the nth term in an exponential sequence.

Example:-
1, 3, 7, 15

Answer 1

To find the nth term expression for the given sequence, observe the pattern that each term is one less than a power of 2. Thus the nth term of the sequence 1, 3, 7, 15 is given by the formula
`T(n) = 2^n - 1.`

Step-by-step explanation:

To find the expression for the nth term in an exponential sequence like 1, 3, 7, 15, we first need to understand that this does not seem to be a typical exponential sequence where each term is obtained by multiplying a fixed number with the previous term. Instead, this sequence follows a pattern where each term is one less than a power of 2 (i.e., an exponential sequence with base 2). For example,
`1 is 2^1 - 1, 3 is 2^2 - 1, 7 is 2^3 - 1`, and so on. Thus, to find the nth term, the pattern implies that the nth term is 2^n - 1.

This can be verified by listing the terms and seeing if they match the given sequence. We have:

• 1st term:
  `2^1` - 1 = 1
• 2nd term:
  `2^2` - 1 = 3
• 3rd term:
  `2^3`- 1 = 7
• 4th term:
  `2^4` - 1 = 15

Hence, the nth term for this specific sequence can be written as T(n) =
`2^n - 1.`

Answer 2

Step-by-step explanation:

Ans:n^th=2n-1

we are going to use the formula of arithmetic sequence.

We need to find the first term of the sequence which is 1 and find the difference between any two number.

Then simply multiply the different by (n-1)

Finally add the result with first term which is 1.