Answer :
Final answer:
The 16th term of the given arithmetic progression is 67. The sum of the first 6 terms is 102.
Explanation:
To find the 16th term of an arithmetic progression (AP), we can use the formula:
an = a1 + (n - 1)d,
where
an is the nth term
a1 is the first term
n is the term number
d is the common difference
In this case, the first term a1 is 7 and the common difference d is 4 (since each term is obtained by adding 4 to the previous term).
Thus, the 16th term is:
a16 = 7 + (16 - 1) * 4
= 7 + 15 * 4
= 7 + 60
= 67
Now, to find the sum of the first 6 terms, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(2a1 + (n - 1)d).
Plugging in the values, we have:
S6 = (6/2)(2 * 7 + (6 - 1) * 4)
= 3(14 + 20)
= 3(34)
= 102
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