Question

Find the sum of the first eighteen terms of the arithmetic sequence where
nth term is a = 15 + 8n.
A) 1438
B) 1638
C) 1836
D) 1783​

Answer 1

a n = 15+8n

a18 =15+8(18)

= 15+144

= 159

For the 1st term,

a 1 = 15+8(1)

= 15+8

= 23

S n = n/2 (a1+ an)

S 18 = 18/2 (23+159)

= 9(182)

= 1638

Here is your answer

Answer 2

Answer :-

• Sum of the first 18 terms of the AP is 1638.

Given :-

• nth term of an AP is a = 15 + 8n

To Find :-

• Sum of first 18 terms.

Solution :-

Here

• nth term = 15 + 8n

We've to find first 2 or 3 terms of the AP

First term :-

Put the value n = 1 in the equation

⇒ 15 + 8(1)

⇒ 15 + 8

⇒ 23

Second term :-

Put the value n = 2 in the equation

⇒ 15 + 8(2)

⇒ 15 + 16

⇒ 31

Now

• First term T1 = 23
• Second term T2 = 31
• Common difference d = T2 - T1 = 31 - 23 = 8

As we know that

• Sum of n terms of an AP is

Sn = n/2 { 2a + (n - 1)d }

Put the values in the formula

⇒ Sn = 18/2 { 2(23) + (18 - 1)8 }

⇒ Sn = 9 { 46 + 136 }

⇒ Sn = 9 × 182

⇒ Sn = 1638

the sum of first 18 terms of the AP is 1638.

Hence, option (b) is correct.