Question

Find the sum of fint sil terms of an AP whose second and third terms are 14 and 18 respectively.​

Answer 1

Answer :-

• Sum of 51 terms = $\boxed{\textsf{\textbf{\red{5610}}}}$

Given :-

• a, a+d, a+2d,......, a+(n-1)d

Terms are in A.P

• Second term = a+d = 14

• Third term = a+2d = 18

To find :-

• Sum of first ‘51’ terms ($\sf{S_{51}}$). (n = 51)

Formula used :-

• $\boxed{\sf{S_n = \dfrac{n}{2} [2a + (n-1)d]}}$

Solution :-

➙ Third term - second term = 18 - 14

$\:\:\:\:\:\:$(a + 2d) - (a + d) = 18 - 14

$\:\:\:\:\:\:$ d = 4

➙ So, a + d = 14

$\:\:\:\:\:\:$ a = 14 - d

$\:\:\:\:\:\:$ a = 14 - 4

$\:\:\:\:\:\:$ a = 10

➪ ${\sf{S_{51} = \dfrac{51}{2} [2a + (51-1)d]}}$

➪ ${\sf{S_{51} = \dfrac{51}{2} [2(10) + (50)(4)]}}$

➪ ${\sf{S_{51} = \dfrac{51}{\cancel{2}} \times \cancel{220}}}$

➪ ${\sf{S_{51} = 51\times 110}}$

➪ $\sf{S_{51} =}$$\sf{\red{5610}}$