The 14th term of an a.p is 1596 while the 25th term is 173 find the 19th term sum of 13th and 36th term product of 6th and 13th term
Just use the formulas you know.
a+13d = 1596
a+24d = 173
solve for a and d, and then find
a+18d
a+12d + a+35d
(a+5d)(a+12d)
To find the 19th term of an arithmetic progression (a.p.), we need to know the common difference. The common difference can be found by subtracting the 14th term from the 25th term.
Common difference = 25th term - 14th term
Common difference = 173 - 1596
Common difference = -1423
Now that we know the common difference, we can find the 19th term by adding the common difference to the 14th term.
19th term = 14th term + (common difference * 5)
19th term = 1596 + (-1423 * 5)
19th term = 1596 - 7115
19th term = -5519
So, the 19th term of the a.p. is -5519.
To find the sum of the 13th and 36th term, we need to add these terms together.
Sum of 13th and 36th term = 13th term + 36th term
Sum of 13th and 36th term = a + (13-1)d + a + (36-1)d
Sum of 13th and 36th term = 2a + 48d
To find the product of the 6th and 13th term, we need to multiply these terms together.
Product of 6th and 13th term = 6th term * 13th term
Product of 6th and 13th term = a + (6-1)d * a + (13-1)d
Product of 6th and 13th term = a + 5d * a + 12d
Product of 6th and 13th term = a^2 + 17ad + 60d^2
Note: In both cases, we need the value of the first term (a) and the common difference (d) in order to calculate the desired results.