Question

find the sum of the numbers from 50th term to 100th term of an ap whose tenth term and twentieth terms are 42 and 82 respectively (THIS question is from arithmetic progression class 10) Please answer quick

Answer 1

The sum of the numbers from 50th term to 100th term of the given AP is 15402

Step-by-step explanation:

Let the first term of AP be a and common difference be d

nth term of AP is given by

$a_n=a+(n-1)d$

Given

10th term and 20th terms are 42 and 82 respectively

Therefore,

$a_{10}=a+(10-1)d$

$\implies a+9d=42$    ............ (1)

$a_{20}=a+(20-1)d$

$\implies a+19d=82$   .............(2)

Subtracting eq (1) from eq (2)

$10d=40$

$\implies d=4$

Putting the value of d in eq (1)

$a+9\times 4=42$

$\implies a+36=42$

$\implies a=6$

From 50th to 100th term toal number of terms = 51

50th term of the AP

$a_{50}=6+(50-1)\times 4$

$a_{50}=6+49\times 4=202$

100th term of the AP

$a_{100}=6+(100-1)\times 4$

$a_{50}=6+99\times 4=402$

We know that if first and last term of an AP is known and number of term is n

Then its sum is given by

$S_n=\frac{n}{2}[\text{First Term}+\text{Last Term}]$

$\implies S_n=\frac{51}{2}(202+402)$

$\implies S_n=\frac{51\times 604}{2}$

$\implies S_n=51\times 302=15402$

Hope this answer is helpful.

Know More:

Q: An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Click Here: https://brainly.in/question/127960

Answer 2

Step-by-step explanation:

The first term of an A.P. is 5 and its 100th term is -292. Find

the 50th term of this A.P..