Question

the sum of first 100 term of sequence 20 30 40​

Answer 1

Answer:

a=20

d=10

S100=100/2[2×20+(100-1)10]

=50[40+99×10]

=50(40+990)

=50×1030

=51500

Answer 2

Answer:

The required sum of first 100 terms is 51,500.

Step-by-step explanation:

Given sequence,

20, 30, 40, ...

Each term is obtained by adding 10 to the previous term. The given sequence is in Arithmetic Progression.

first term, a = 20

common difference, d = 30 – 20 = 10

Sum of first n terms of an A.P is given by,

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

To find the sum of first 100 terms of the given sequence, put n = 100 and substitute the other values

= 100/2 [2(20) + (100 – 1) (10) ]

= 50 [40 + 99(10)]

= 50 [40 + 990]

= 50(1030)

= 51500

Therefore, the required sum of first 100 terms is 51,500.