Question

in an AP given A=-4, d=3 find its 20 term and sum of first 20 terms

Answer 1

Answer:

20th term in AP = 53

Sum of the first 20 terms = 490      

Step-by-step explanation:

Given data

In a AP ⇒ First term A = - 4 and common difference d = 3  

here we need to find 20th term and sum of the 20 terms

⇒ in AP nth term = $T_{ n}$ =  A + (n - 1) d

⇒ 20th term = $T_{20}$ = (- 4) + ( 20 - 1) (3)

                             =  - 4 + (19)(3)

                             = - 4 + 57 = 53  

⇒ Sum of the n terms = S= $\frac{n}{2} [2a +(n-1)d]$  

⇒ Sum of 20 terms = $\frac{20}{2}$ [ 2(-4) +(20 - 1) (3)]

                                =  10 [ -8 + 19(3)]

                                = 10 [-8 + 57 ]  

                                = 10 [49]  = 490            

Answer 2

Given,

In an arithmetic progression A = -4, d =3.

To find,

Find its 20th term and the sum of first 20 terms.

Solution,

The 20th term of an Arithmetic Progression-

⇒  a20 = a + 19d

⇒  a20 = -4 + 19(3)

⇒  a20 = -4 + 57

⇒  a20 = 53

The sum of Arithmetic Progression can be calculated as-

Sn = n/2{2a+(n-1)d}

Sn = 20/2{2(-4)+(20-1)3}

The sum of first 20 terms of the AP is -

S20 = 10{-8+57}

S20 = 10{49}

S20 = 490

Therefore, the sum of the first 20 terms of Arithmetic Progression is 490, the 20th term of the Arithmetic Progression is a20 = 53.