Question

What is the sum of the first 45 terms of the arithmetic sequence 1, 4, 7, . . . ?

Answer 1

Step-by-step explanation:

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Answer 2

• GIVEN:-

Arithmetic sequence 1, 4, 7, . . .

• TO FIND:-

Sum of first 45 terms.

• SOLUTION:-

To find the sum of n terms of AP we use,

$\large\boxed{\sf{S_{n}=\dfrac{n}{2}[2a+(n-1)\times\:d]}}$

where,

• a is the first term
• n is the terms of AP
• d is the common difference

Therefore for this sequence,

• d = 4 - 1 = 3
• a = 1
• n = 45

Putting the values,

$\large\Rightarrow{\sf{S_{n}=\dfrac{n}{2}[2a+(n-1)\times\:d]}}$

$\large\Rightarrow{\sf{S_{45}=\dfrac{45}{2}[(2\times1)+(45-1)\times3]}}$

$\large\Rightarrow{\sf{S_{45}=\dfrac{45}{2}[2+44\times3]}}$

$\large\Rightarrow{\sf{S_{45}=\dfrac{45}{2}[2+132]}}$

$\large\Rightarrow{\sf{S_{45}=\dfrac{45}{2}\times134}}$

$\large\Rightarrow{\sf{S_{45}=\dfrac{45}{\cancel{2}}\times\cancel{134}\:\:\:\:67}}$

$\large\Rightarrow{\sf{S_{45}=45\times67}}$

$\large\Rightarrow{\sf{S_{45}=3015}}$

$\large{\pink{\underline{\boxed{\therefore{\sf{\pink{Sum\:of\:first\:45\:terms\:of\:the\:arithmetic\:sequence\:1,4,7,....\:is\:3015.}}}}}}}$