Final answer:
To find the first term, common difference, and 20th term of an A.P., we can use the given information about the 10th and 17th terms. Substitute the known values into the formula and solve the equations to find a1 and d. Use the values in the formula to find the 20th term.
Step-by-step explanation:
To find the first term, the common difference, and the 20th term of an arithmetic progression (A.P.), we can use the given information about the 10th and 17th terms.
The formula to find the nth term of an A.P. is: an = a1 + (n-1)d
Using this formula, we can substitute the known values:
For the 10th term: 7 = a1 + (10-1)d
For the 17th term: -7 = a1 + (17-1)d
Solving these two equations simultaneously will give us the values of a1 (the first term) and d (the common difference).
Substituting these values in the formula will help us find the 20th term: a20 = a1 + (20-1)d