Solve the following the first term of an AP is 5 and the common difference is -3/2 find the term whose value is -20 whole number 1/2
The formula for the nth term (Tn) of an arithmetic progression (AP) is given by:
Tn = a + (n-1)d
where a is the first term and d is the common difference.
In this case, the first term (a) is 5 and the common difference (d) is -3/2.
Let's substitute these values into the formula and solve for n when the term value is -20:
-20 = 5 + (n - 1)(-3/2)
We can simplify this equation by multiplying through by 2 to eliminate the fraction:
-40 = 10 - 3(n - 1)
Next, distribute the -3 to both terms inside the parentheses and simplify:
-40 = 10 - 3n + 3
Combine like terms:
-40 = 13 - 3n
Subtract 13 from both sides:
-53 = -3n
Divide by -3:
n = 17.67
Since we are looking for a whole number term, we need to round up to the nearest whole number.
Therefore, the term whose value is -20 (to the nearest whole number) is the 18th term of the arithmetic progression.