Question

the first and last term arithmetic sequence are 9 and 165 respectively.if the sum of all the terms of the arithmetic sequence is 3480,find the number of terms and the common difference of this arithmetic sequence​

Answer 1

Required Answer:-

• first term =a=9
• Last term =l=165
• Sn=3480

As we know that in a AP

`{:}\longrightarrow`
`\sf S_n={\frac {1}{2}}(a+l)n`

• Substitute the values

`{:}\longrightarrow`
`\sf 3480={\frac {1}{2}} (9+165)n`

`{:}\longrightarrow`
`\sf 3480={\frac {1}{2}}(174)n`

`{:}\longrightarrow`
`\sf 3480={\frac {174}{2}}n`

`{:}\longrightarrow`
`\sf 3480=87n`

`{:}\longrightarrow`
`\sf n={\frac {3480}{87}}`

`{:}\longrightarrow`
`\sf n=40`

`\therefore`Number of terms=40.

Answer 2

• 40 terms

Explanation:

Sum of n terms formula:

• Sn = 1/2n(a1 + an)

Solving for n

• 3480 = 1/2n(9 + 165)
• 3480 = 87n
• n = 3480/87
• n = 40