Find the 6th and 15th term of the ap whose first term is 6 and common difference is 7
In AP:
an = a ( n - 1 ) d
where
a = first term
d = common difference
In this case a = 6 , d = 7
a6 = a + 5 d
a15 = a + 14 d
Calculate this.
To find the 6th and 15th term of the arithmetic progression (AP) with a first term of 6 and a common difference of 7, you can use the formula for the nth term of an AP.
The formula is given by:
nth term = first term + (n - 1) * common difference
To find the 6th term:
n = 6
first term = 6
common difference = 7
6th term = 6 + (6 - 1) * 7
= 6 + 5 * 7
= 6 + 35
= 41
Therefore, the 6th term of the AP is 41.
To find the 15th term:
n = 15
first term = 6
common difference = 7
15th term = 6 + (15 - 1) * 7
= 6 + 14 * 7
= 6 + 98
= 104
Therefore, the 15th term of the AP is 104.
To find the 6th and 15th terms of an arithmetic progression (AP) with a first term of 6 and a common difference of 7:
Step 1: Find the formula for the nth term of an AP.
The formula for the nth term (Tn) of an AP is:
Tn = a + (n - 1) * d
Where:
Tn = nth term
a = first term
n = term number
d = common difference
Step 2: Calculate the 6th term.
Plug in the values into the formula:
T6 = 6 + (6 - 1) * 7
= 6 + 5 * 7
= 6 + 35
= 41
Therefore, the 6th term of the AP is 41.
Step 3: Calculate the 15th term.
Again, plug in the values into the formula:
T15 = 6 + (15 - 1) * 7
= 6 + 14 * 7
= 6 + 98
= 104
Therefore, the 15th term of the AP is 104.