Question

What is the difference between the sums of first 10 terms of the arithmetic sequences 4, 10, 16, ... and 15, 21, 27, ... ?​

Answer 1

Answer:

110

Explanation:

Given two A. P.s

• 4, 10, 16. . . . .
• 15, 21, 27 . . . . .

We know,

Sum of nth term of an A. P. = n/2[2a + (n – 1)d]

Where,

• n denotes the number of terms.
• a is the first term.
• d denotes the common difference.

Then, sum of 10 terms of first A. P. :-

→ n/2[2a + (n - 1)d]

→ 10/2[2(4) + (10 - 1)6]

→ 5[8 + (9)6]

→ 5[8 + 54]

→ 5[62]

→ 310

And also, sum of 10 terms of second A. P. :-

→ n/2[2a + (n – 1)d]

→ 10/2[2(15) + (10 - 1)6]

→ 5[30 + (9)6]

→ 5[30 + 54]

→ 5[84]

→ 420

Their difference is :-

→ 420 - 310

→ 110

∴ Required answer: 110