Question

How many terms of the AP 63,60,57..must taken as the sum is 693
Step by step pls

Answer 1

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Answer 2

$<b>Answer:</b>$

21 terms or 22 terms

$<b>Step-by-step explanation:</b>$

$<b>Formula Needed:</b>$

an = a1 + (n - 1)d

Sn = n/2 (a1 + an)

$<b><i>STEP 1: Find the common difference:</b></i>$

Common Difference = a2 - a1

Common Difference = 60 - 63

Common Difference = -3

STEP 2: Find the nth term:

d = -3, a1 = 63

an = a1 + (n - 1)d

an = 63 + ( n - 1)(-3)

an = 63 - 3n + 3

an = 66 - 3n

STEP 3: Solve n

Sn = n/2 (a1 + an)

693 = n/2 (63 + (66 - 3n) )

693 = n/2 (63 + 66 - 3n)

693 = n/2 (129 - 3n)

1386 = n(129 - 3n)

1386 = 129n - 3n²

3n² - 129n + 1386 = 0

3(n - 21)(n - 22) = 0

n = 21 or n = 22

Answer: Both 21 terms and 22 terms will give a sum of 693