The sum of the first 20 terms of an arithmetic progression whose first term is 5 and common difference is 4 is _____.

Given:

First term 'a' = 5, common difference 'd' = 4

Number of terms 'n' = 20

Concept:

Arithmetic progression:

• Arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.
• The fixed number is called common difference 'd'.
• It can be positive, negative or zero.

Formula used:

n^th term of AP 

T_n = a + (n - 1)d

The Sum of n terms of AP is given by

\(S = \dfrac{n}{2}[2a + (n-1)d]\)

\(S = \dfrac{n}{2}( a + l)\)

Where, 

a = first term of AP, d = common difference, l = last term 

Calculation:

We know that sum of n terms of AP is given by

\(S = \dfrac{n}{2}[2a + (n-1)d]\)

\(⇒ S = \dfrac{20}{2}[2× 5 + (20-1)× 4]\)

⇒ S = 10(10 + 76)

⇒ S = 860

Hence, the sum of 20 terms given AP will be 860.

We know that n^th term of AP is given by

Tn = a + (n - 1)d

If l is the 20th term (last term) of AP, then

l = 5 + (20 - 1) × 4 = 81

So the sum of AP

\(S = \dfrac{n}{2}( a + l)\)

\(⇒ S = \dfrac{20}{2}(5 + 81)\)

⇒ S = 860