What is the sum of the first 10 terms of the sequence defined by a_n = 4n - 3

Solution:

Given, a_n = 4n - 3

We have to find the sum of the first 10 terms of the sequence.

a₁ = 4(1) - 3 = 4 - 3 = 1

a₂ = 4(2) - 3 = 8 - 3 = 5

a₃ = 4(3) - 3 = 12 - 3 = 9

a₄ = 4(4) - 3 = 16 - 3 = 13

a₅ = 4(5) - 3 = 20 - 3 = 17

a₆ = 4(6) - 3 = 24 - 3 = 21

a₇ = 4(7) - 3 = 28 - 3 = 25

a₈ = 4(8) - 3 = 32 - 3 = 29

a₉ = 4(9) - 3 = 36 - 3 = 33

a₁₀ = 4(10) - 3 = 40 - 3 = 37

The sum of the terms = 1+ 5 + 9 + 13 + 17 + 21 + 25 + 29 + 33 + 37

Here we see the sequence is in Arithmetic Progression with the common difference 4. Thus we can use the formula to find the sum of n terms in an AP.

S_n = n(a+l)/2 where a and l are the first and the last terms respectively.

Here a₁ = 1 and a₁₀ =37

Thus S₁₀ = 10(1 +37)/2

= 5(38)

=190

Therefore, the sum of the first 10 terms is 190.

---

What is the sum of the first 10 terms of the sequence defined by a_n = 4n - 3

Summary:

The sum of the first 10 terms of the sequence a_n = 4n - 3 is 190.