Question

if the3rd term of AP is 18band 17th term is42 then the first term is​

Answer 1

✰ Given:-

• $\sf{3rd \; term \; of \; AP \; ( \sf a_3 ) = 18} \; \; \; \; -----(1)$
• $\sf{17th \; term \; of \; AP \; ( \sf a_{17} )= 42} \; \; \; -----(2)$

✰ To find:-

• First term (a) = ?

✰Solution:-

★ From eq(1) and eq(2):-

✧ Using elimination method:-

a + 2d = 18

a + 16d = 42

_____________

= -14d = -24

$\implies \sf{d = \cancel{\dfrac{-24}{-14}}}$

$\implies \sf{d = \dfrac{12}{7}}$

★ Putting value of d in eq. (1):-

• $\sf{ \sf a_3 = 18}$

• $\sf{a + 2d = 18}$

• $\sf{ a + 2 × \dfrac{12}{7} = 18}$

• $\sf{ a + \dfrac{24}{7} = 18}$

• $\sf{ a = 18 - \dfrac{27}{7}}$

• $\sf{ a = \dfrac{126 - 27}{7}}$

• $\sf{ a = \dfrac{99}{7}}$

$\rule{200}{2}$