What is the sum of the first 30 terms of this arithmetic sequence? 6, 13, 20, 27, 34, …

Solution:

It is given that the terms are in arithmetic sequence.

The first term = a = 6 and the common difference = d = 7,

We have to find the sum of first 30 terms in AP,

Then,

S_n = n/2 [2a + (n-1)d]

Substituting the values

S₃₀ = 30/2 [ 2 x 6 + (30 - 1) x 7 ]

= 15 [ 12 + 29 x 7 ]

By further calculation

= 15 [ 12 + 203 ]

= 15 x 215

= 3225

Therefore, the sum of the first 30 terms is 3225.

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What is the sum of the first 30 terms of this arithmetic sequence? 6, 13, 20, 27, 34, …

Summary:

The sum of the first 30 terms of this arithmetic sequence 6, 13, 20, 27, 34, … is 3225.