Question

The 5th term of an AP is - 3 and its
common difference is -4. The sum of its first ten terms is? ​

Answer 1

Answer:

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Answer 2

Solution :

$\bigstar$ Firstly, we know that formula of the A.P;

$\boxed{\bf{a_n=a+(n-1)d}}}}$

• a is the first term.
• d is the common difference.
• n is the term of an A.P.

A/q

$\longrightarrow\sf{a_5=-3}\\\\\longrightarrow\sf{a+(5-1)(-4)=-3\:\:\:\:[Given,d=-4]}\\\\\longrightarrow\sf{a+4\times (-4)=-3}\\\\\longrightarrow\sf{a+(-16)=-3}\\\\\longrightarrow\sf{a-16=-3}\\\\\longrightarrow\sf{a=-3+16}\\\\\longrightarrow\bf{a=13}$

$\bigstar$ secondly, we know that formula of the sum of an A.P;

$\boxed{\bf{S_n=\frac{n}{2} \bigg[2a+(n-1)d\bigg]}}}$

$\longrightarrow\sf{S_{10}=\cancel{\dfrac{10}{2}} \bigg[2(13)+(10-1)(-4)\bigg]}\\\\\longrightarrow\sf{S_{10}=5[26+9(-4)]}\\\\\longrightarrow\sf{S_{10}=5[26-36]}\\\\\longrightarrow\sf{S_{10}=5\times (-10)}\\\\\longrightarrow\bf{S_{10}=-50}$

Thus;

The Sum of first 10th term will be -50 .