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

Answer:

• 40 terms

Step-by-step 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

Answer 2

Answer:

Required Answer:-

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

As we know that in a AP

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

• Substitute the values

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

${:}\longrightarrow$$\sf 3480={\dfrac {1}{2}}(174)n$

${:}\longrightarrow$$\sf 3480={\dfrac {174}{2}}n$

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

${:}\longrightarrow$$\sf n={\dfrac {3480}{87}}$

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

$\therefore$Number of terms=40.