The sum of 5 numbers in an Ap is 30 sum of their squares is 220 find - Math - Arithmetic Progressions

Question

The sum of 5 numbers in an Ap is 30 & sum of their squares
is 220 find the third tern-
*** Plzzzzz solve with all steps ***

Lalit Mehra · Accepted Answer

Dear Student! Let five numbers in A P be a â€“ 2d, a â€“ d, a, a + d and a + 2d Given (a â€“ 2d) + (a â€“ d) + a + (a + d) + (a + 2d) = 30 $∴ 5 a = 30 \Rightarrow a = \frac{30}{5} = 6 G i v e n, (a - 2 d)^{2} + {(a - d)}^{2} + a^{2} + {(a + d)}^{2} + {(a + 2 d)}^{2} = 220$ Putting a = 6, we get $(6 - 2 d)^{2} + (6 - d)^{2} + (6)^{2} + (6 + d)^{2} + (6 + 2 d)^{2} = 220 \Rightarrow 36 + 4 d^{2} - 24 d + 36 + d^{2} - 12 d + 36 + 36 + d^{2} + 12 d + 36 + 4 d^{2} + 24 d = 220 \Rightarrow 180 + 10 d^{2} = 220 \Rightarrow 10 d^{2} = 220 - 180 = 40 \Rightarrow d^{2} = 4 \Rightarrow d = \pm 2$ When a = 6 and d = 2, we get $a - 2 d = 6 - 2 \times 2 = 6 - 4 = 2 a - d = 6 - 2 = 4 a = 6 a + d = 6 + 2 = 8 a + 2 d = 6 + 2 \times 2 = 6 + 4 = 10$ when a = 6 and d = â€“2, we get $a - 2 d = 6 - 2 \times (- 2) = 6 + 4 = 10 a - d = 6 - (- 2) = 6 + 2 = 8 a = 6 a + d = 6 + (- 2) = 6 - 2 = 4 a + 2 d = 6 + 2 \times (- 2) = 6 - 4 = 2$ Five numbers in A P are 2, 4, 6, 8 and 10 Thus, the third number is 6 Cheers!

The sum of 5 numbers in an Ap is 30 & sum of their squares is 220. find the third tern- *** Plzzzzz solve with all steps ***

The sum of 5 numbers in an Ap is 30 & sum of their squares is 220. find the third tern-

* Plzzzzz solve with all steps *