The sum of the first 16 terms for the given arithmetic sequence will be 328.
<h3>What is Arithmetic progression?</h3>
An arithmetic progression is when every two succeeding terms in a sequence have the same difference (AP).
For example ;
Natural number = 1,2,3,4,5,6,7,8...
Now it has the same difference between any two consecutive terms d =2-1 = 3-2.
The nth term of AP is given by,
= a + (n - 1) d
Given
a₄ = 7
So,
a + 3d = 7
And
a₇ = 16
So,
a + 6d = 16
By substituting equations 1 to 2
a = -2 and d = 3
The Sum of n terms is given by
= N/2[ 2a + (n - 1)d]
So,
= 16\2[2(-2) + ( 16 - 1)3]
= 328
Hence the sum of the first 16 terms will be 328.
For more about Arithmetic progression
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