Question

If the second term in an arithmetic sequence is 4, and the tenth term is 15, what is the first term in the sequence?​

Answer 1

Let first term of Arithmetic Progression be a and its common difference be d.

According to the question:-)

$2nd\: term = a_2 = 4 \\ \\ i.e. \\ \\ a + d = 4...............(1) \\ \\ and \\ \\ 10th \: term = a_{10} = 15 \\ \\ i.e. \\ \\ a + 9d = 15................(2)$

$9 \times (1) -(2) \implies \\ \\ 8a = 21 \\ \\ a = \frac{21}{8}$

So first term of the AP will be :-)

$\huge {\dfrac{21}{8}}$

Answer 2

$\frac{21}{8}$