Question

The first term of an AP is 5,the last terms is 45 and the sum is 400 find the number of
terms and the common difference.​

Answer 1

Solution

Given :-

• a = 5
• L = 45
• Sn = 400

Find :-

• n = ?
• d = ?

Explanation

Using Formula

★Sn = n(a + L)/2

Keep all value,

==> Sn = n × (5 + 45)/2

==> 400 × 2 = n (50)

==> 800 = n × 50

==> n = 800/50

==> n = 16

Now, Calculate common Defference.

Using Formula

★ Sn = n[ 2a + (n - 1)d]/2

Keep Value,

==> 400 = 16[ 2 × 5 + ( 16 - 1)d]/2

==> 400 = 8 [ 10 + 15d]

==> 400/8 = 10 +15d

==> 50 - 10 =15d

==> 15d = 40

==> d = 40/15

==> d = 2.67

Hence

• Common Defference will be d = 2.67
• Number of terms n = 16

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