if Sn is the first n terms of a series given by Sn2-1 find the nth terms
2 find the sum of all numbers between 5 and 130 which are divisible by 4?
To find the nth term of the series given by Sn = 2n - 1, you can simply substitute the value of n into the formula.
1. Substitute the value of n into the formula Sn = 2n - 1
2. The nth term of the series is 2n - 1.
For example, if you want to find the 5th term, substitute n = 5 into the formula:
S5 = 2(5) - 1 = 10 - 1 = 9
Therefore, the 5th term of the series is 9.
Regarding your second question, to find the sum of all numbers between 5 and 130 that are divisible by 4, you can calculate it by summing up the numbers in the range.
1. Identify the first number divisible by 4 within the range. In this case, it is 8 (the smallest number greater than 5 divisible by 4).
2. Identify the last number divisible by 4 within the range. In this case, it is 128 (the largest number less than 130 divisible by 4).
3. Calculate the number of terms in the range by subtracting the first number from the last number and then adding 1.
Number of terms = (128 - 8) / 4 + 1 = 32 + 1 = 33
4. Use the formula for the sum of an arithmetic series to calculate the sum.
Sum = (number of terms / 2) * (first term + last term)
Sum = (33 / 2) * (8 + 128) = 16.5 * 136 = 2244
Therefore, the sum of all numbers between 5 and 130 that are divisible by 4 is 2244.