The 16th term of an Ap is 93 and its common Difference is 6 find the first term of the Ap and hence calculate the 30th term of the Ap
a1 = a16-15d = 93 - 15*6 = ____
a30 = a16+14d = 93 + 14*6 = _____
To find the first term of the Arithmetic Progression (AP), we can use the formula:
\[a_n = a + (n-1)d\]
where \(a_n\) is the \(n\)th term, \(a\) is the first term, \(d\) is the common difference, and \(n\) is the position of the term.
Given that the 16th term \(a_{16}\) is 93 and the common difference \(d\) is 6, we can substitute these values into the formula:
\[a_{16} = a + (16-1) \cdot 6\]
Simplifying the equation:
\[93 = a + 15 \cdot 6\]
\[93 = a + 90\]
Subtracting 90 from both sides:
\[a = 3\]
Therefore, the first term of the AP is 3.
To find the 30th term \(a_{30}\), we can again use the formula:
\[a_n = a + (n-1)d\]
Substituting the values:
\[a_{30} = 3 + (30-1) \cdot 6\]
Simplifying the equation:
\[a_{30} = 3 + 29 \cdot 6\]
\[a_{30} = 3 + 174\]
\[a_{30} = 177\]
Therefore, the 30th term of the AP is 177.