Question

In an AP of 21 terms, the sum of the first 3 terme is 33 and that of the middle 3 it 3te is 75. What is the aum of the AP? A. 955 B. -1155 C. 525 D.

Answer 1

CORRECT QUESTION:

In an Ap of 21 terms ,the sum of the first 3 terms is -33 and that of the middle 3 is 75.what is the sum of the Ap ?

ANSWER:

SUM OF 21 TERMS IS EQUAL TO 525

FORMULA:

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

$s_n$ = n/2 (2a + (n - 1) d)

GIVEN:

$a_1+a_2+a_3$ = a + a + d + a + 2d = -33

MIDDLE TERM = (n+1)/2

n = 2

MIDDLE TERM = (21 + 1)/2

MIDDLE TERM = 11

$a_{10}+a_{11}+a_{12}$ => a + 9d + a + 10 + a + 11d = 75

TO FIND:

THE SUM OF AP.

EXPLANATION:

3a + 3d = -33

Divide by three on both sides

a + d = - 11

a = -11 - d

Also

3a + 30d = 75

Divide by three on both sides

a + 10d = 25

Substitute a = -11 - d

-11 - d + 10d =25

9d = 36

d = 4

Substitue d = 4 in a + d = - 11

a + 4 = -11

a = -15

$s_{21}$ = 21/2(2(-15) + (21 - 1) 4)

$s_{21}$ = 21/2(-30 + (20) 4)

$s_{21}$ = 21/2 (-30 + 80)

$s_{21}$ = 21/2(50)

$s_{21}$ = 21 × 25

$s_{21}$ = 525

SUM OF 21 TERMS IS EQUAL TO 525.