Solve for the 1st term of the arithmetic sequence whose 33rd term is -2p and whose 61st term is 26p.

a+32d = -2p

a+ 60d = 26p
subtract:
28d = 28p
d = p

a + 32p = -2p
a = -34p

No

Wrong answer

To solve for the 1st term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence.

The formula for the nth term of an arithmetic sequence is given by:
An = A1 + (n - 1)d

Where:
An represents the nth term of the sequence
A1 represents the 1st term of the sequence
n represents the position of the term in the sequence
d represents the common difference between consecutive terms

In this case, we are given the 33rd term and the 61st term of the sequence. So we can set up two equations using the formula above and solve for A1.

First, we have:
-2p = A1 + (33 - 1)d

And second, we have:
26p = A1 + (61 - 1)d

Now, we can subtract the two equations to eliminate the A1 term:
26p - (-2p) = (61 - 1)d - (33 - 1)d

This simplifies to:
28p = 60d

Now, we can simplify the equations to solve for A1:

-2p = A1 + 32d
26p = A1 + 60d

By substituting the value of 60d from the second equation into the first equation, we get:

-2p = A1 + (26p - A1)
-2p = 26p

Now, we can solve for p:

-2p - 26p = 0
-28p = 0
p = 0

Substituting p = 0 into any of the equations, we can solve for A1. Let's use the second equation:

26(0) = A1 + 60d
0 = A1

Therefore, the 1st term of the arithmetic sequence is equal to 0.