1.

The 17th term of an A.P. is 7 more than the 10th term. Find the common difference (d).​

Answer»

ong>Answer:

  • d = 1

Step-by-step EXPLANATION:

GIVEN:

  • The 17th term of an A.P. is 7 more than the 10TH term.

To find:

  • Common difference

Solution:

In this kind of question, we are going to arrive an equation. From the equation, we will get the value of Common Difference(d), which is our REQUIRED answer.

\begin{gathered}\underline{\tt{Formula\:for\:nth\:term:}}\\\\\\:\implies{\boxed{\pink{\sf{a_n = a+(n-1)d}}}}\\\\\\\underline{\tt{Hence,}}\\\\\\:\implies\sf{a_{17} = a+(17-1)d}\\\\\\:\implies\sf{a_{17} = a+16d}\\\\\\\underline{\tt{Similarly,}}\\\\\\:\implies\sf{a_{10} = a+(10-1)d}\\\\\\:\implies\sf{a_{10} = a+9d}\end{gathered}

\begin{gathered}\dag{\underline{\textit{\textbf{According\: to\: the\: question:}}}}\\\\\\:\implies\sf{a_{17} = 7+a_{10}}\\\\\\:\implies\sf{a+16d = 7+a+9d}\\\\\\:\implies\sf{\cancel{a}+16d = 7+\cancel{a}+9d}\\\\\\:\implies\sf{16d = 7+9d}\\\\\\:\implies\sf{16d-9d = 7}\\\\\\:\implies\sf{7d = 7}\\\\\\:\implies\sf{d = \dfrac{7}{7}}\\\\\\:\implies\boxed{\red{\bf{d = \frak{1}}}}\checkmark\\\\\\\therefore\underline{\sf{The\:value\:of\:Common\:Difference\:is\:1}}\end{gathered}


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