Question

The sum of the first n term of an AP is 252.If the first term is -16,and the last term is 72,find the number of terms in the series.

Answer 1

Answer:

• The number of terms in the series = 9

Step-by-step explanation:

Given that:

• The sum of the first n term of an AP is 252.
• First term, a = - 16
• Last term, l = 72

To Find:

• The number of terms in the series.

• Let the number of term in the series be n.

Formula used:

• Sum of the first n term = n × (a + l)/2

Finding the value of n:

Sum of the first n term = n × (a + l)/2

• Substituting the values.

→ 252 = n × (- 16 + 72)/2

→ 252 × 2 = n × 56

→ n = (252 × 2)/56

→ n = 9

∴ The number of terms in the series = 9

Answer 2

Given

• Sum of first n terms of an AP = 252
• The first term = -16
• The last term = 72

To find

• The number of terms in the series

Solution

⇨ a = -16

⇨ l = 72

⇨ n = ?

We know, sum of n terms in an AP is given by the formula :-

• n (a + l)/2

Substituting the values, we get :-

• 252 = n (-16 + 72)/2
• 252 (2) = n (56)
• 504 = 56n
• n = 504/56
• n = 9

Hence, the number of terms in the series are 9