Question

The following is an AP 9,x,y,z,23 find the valu of x,y,z, the 60th term the next three terms after 25 above

Answer 1

The question involves solving for missing values in an Arithmetic Progression (AP) and finding specific terms within the AP using the nth term formula.

Step-by-step explanation:

The student is asking about an Arithmetic Progression (AP) where the terms 9, x, y, z, and 23 are given, and the task is to find the values of x, y, z. Additionally, the 60th term and the next three terms after the term greater by 25 from the last term given (23) are also requested. To find these values, a common difference should be calculated first, and then the formula for the nth term of an AP, which is an = a1 + (n - 1)d, should be used, where a1 is the first term of the AP and d is the common difference.

Answer 2

To find the value of x, y, z, and the 60th term of the AP 9,x,y,z,23 sequence, we need to follow these steps:

1. Find the common difference (d) by subtracting the first term (a) from the second term (a+d):

d = a + d - a = 23 - 9 = 14

2. Calculate the value of x:

x = a + (n-1)d = 9 + (60-1)14 = 206

3. Find the value of y:

y = a + nd = 9 + 60(14) = 876

4. Determine the value of z:

z = a + (n+1)d = 9 + 61(14) = -288

5. Compute the 60th term:

T60 = a + (n-59)d = 9 + 59(14) = 876

Explanation:

The sequence AP 9,x,y,z,23 is an arithmetic progression (AP) with first term (a) equal to 9, common difference (d) equal to 14, and last term (L) equal to 23. To find the values of x, y, z, and the 60th term of this sequence, we follow these steps:

Step 1: Find the common difference (d) by subtracting the first term (a) from the second term (a+d):

d = a + d - a = 23 - 9 = 14

Step 2: Calculate the value of x by substituting n as 60 and d as calculated in step 1 in the formula for x:

x = a + (n-1)d = 9 + (60-1)14 = 206

Step 3: Find the value of y by substituting n as 60 and d as calculated in step 1 in the formula for y:

y = a + n*d = 9 + 60*14 = 876

Step 4: Determine the value of z by substituting n as 61 and d as calculated in step 1 in the formula for z:

z = a + (n+1)*d = 9 + 61*14 = -288

Step 5: Compute the value of T60 by substituting n as 59 and d as calculated in step 1 in the formula for Tn:

T60 = a + (n-59)*d = 9 + 59*14 = 876

In this sequence, we observe that z is negative because n is greater than L/d. This indicates that z is beyond L and hence it is not part of this sequence. The sequence starts from a and ends at L. The values obtained for x, y, and T60 are all positive because they are within this range. The values obtained for x and y are quite large because they are far away from a and closer to L. The value obtained for T60 is equal to y because they both represent the same position in this sequence.