Question

A7=23 ; a25=59 a2=?​

Answer 1

A7 = A1+6d

A25 = A1+24d

{A1+6d = 23

{A1+24d = 59

24d-6d = 59-23

18d = 36

d = 2

A1+12 = 23

A1 = 11

A2 = A1+d = 11+2 = 13

Answer 2

To find the value of "a2," we need more information about the pattern or rule that governs the sequence. From the given examples, we can't determine the pattern with certainty. However, let's try to explore some possibilities based on the information provided:

1. If the sequence follows a linear pattern: We can find the slope (m) using two given points: (7, 23) and (25, 59). m = (59 - 23) / (25 - 7) = 36 / 18 = 2

Now, using the point-slope form equation for a line: y - y1 = m(x - x1), where (x1, y1) is any point on the line. Let's use the point (7, 23): y - 23 = 2(x - 7) y - 23 = 2x - 14 y = 2x + 9

Now, for a2, we plug x = 2 into the equation: a2 = 2 * 2 + 9 a2 = 4 + 9 a2 = 13

So, if the sequence follows a linear pattern, a2 would be 13.

2. If the sequence follows a quadratic pattern: We can try fitting a quadratic equation of the form y = ax^2 + bx + c to the given points.

Using (7, 23): 23 = a * 7^2 + b * 7 + c 23 = 49a + 7b + c

Using (25, 59): 59 = a * 25^2 + b * 25 + c 59 = 625a + 25b + c

Now we have a system of three equations:

1. 23 = 49a + 7b + c
2. 59 = 625a + 25b + c

Subtracting equation 1 from equation 2 to eliminate c: 59 - 23 = 625a + 25b + c - (49a + 7b + c) 36 = 576a + 18b

Divide by 18 to simplify: 2 = 32a + b

Now we need another equation to solve for a and b. Without more information or additional data points, we can't uniquely determine the values of a and b. Hence, we can't find the exact value of a2.

Please provide more information about the pattern or any additional data points if available, and I'd be happy to help you further!