# Ex.5.3 Q13 Arithmetic Progressions Solution - NCERT Maths Class 10

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## Question

Find the sum of first $$15$$ multiples of $$8.$$

Video Solution
Arithmetic Progressions
Ex 5.3 | Question 13

## Text Solution

What is Known?

Multiples of $$8$$

What is Unknown?

Sum of first $$15$$ multiples of $$8,$$ $${S_{15}}$$

Reasoning:

Sum of the first $$n$$ terms of an AP is given by $${S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right]$$ Where $$a$$ is the first term, $$d$$ is the common difference and $$n$$ is the number of terms.

Steps:

The multiples of $$8$$ are $$8, 16, 24, 32, \dots$$

These are in an A.P.,

Hence,

• First term, $$a = 8$$
• Common difference, $$d = 8$$
• Number of terms, $$n = 15$$

As we know that Sum of $$n$$ terms,

\begin{align}{S_n} &= \frac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right]\\{S_{15}} &= \frac{{15}}{2}\left[ {2 \times 8 + \left( {15 - 1} \right)8} \right]\\ &= \frac{{15}}{2}\left[ {16 + 14 \times 8} \right]\\ &= \frac{{15}}{2}\left[ {16 + 112} \right]\\& = \frac{{15}}{2} \times 128\\ &= 15 \times 64\\& = 960\end{align}

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