Question

Please solve this question guys.... ❤

Two APs have the same common difference .If the first term of these two APs be 3 and 8 respectively ,find the difference between the sums of theirs first 50 terms. ​

Answer 1

Answer:

→ 250 .

Step-by-step explanation:

Given :-

→ a₁ = 8.

→ a'₁ = 3.

→ d₁ = d'₁ .

To find :-

→ S₅₀ - S'₅₀ .

Solution :-

Let a₁ and a'₁ be the two APs.

Then, a₁ = 8 and a'₁ = 3.

Let d be the common difference of the two APs.

Then,

→ S₅₀ - S'₅₀ .

[ $S_n$ = n/2 ( 2a + ( n - 1 )d . ]

= [ 50/2 ( 2 × 8 + ( 50 - 1 )d ] - [ 50/2 ( 2 × 3 + ( 50 - 1 )d ] .

= [ 25 ( 16 + 49d ) ] - [ 25 ( 6 + 49d ].

= [ 400 + 1225d ] - [ 150 + 1225d ].

= 400 + 1225d - 150 - 1225d .

= 400 - 150 .

= 250.

Hence, 250 is the difference between the sum of their first 50 terms.

Answer 2

Refers to attachment ♡♡~