Let a1, a2, a3, ldots be an arithmetic progression with a1=7 and common difference 8 . Let T1, T2, T3, ldots be such that T1=3 and Tn+1-Tn=an for n ≥ 1. Then, which of the following is/are TRUE ?

Question

Let a1, a2, a3, ldots be an arithmetic progression with a1=7 and common difference 8 . Let T1, T2, T3, ldots be such that T1=3 and Tn+1-Tn=an for n ≥ 1. Then, which of the following is/are TRUE ? (A) T20=1604 (B)  displaystyle∑ k =120 T k =10510 (C) T30=3454 (D)  displaystyle∑ k =130 T k =35610

Tardigrade Admin · Accepted Answer

a 1=7, d =8 T n +1- T n = a n ∀ n ≥ 1 S n = T 1+ T 2+ T 3+ ldots+ T n -1+ T n S n = T 1+ T 2+ T 3+ ldots+ T n -1+ T n on subtraction T n = T 1+ a 1+ a 2+ ldots+ a n -1 T n =3+( n -1)(4 n -1) T n =4 n 2-5 n +4 ∑ k =1 n T k =4 ∑ n 2-5 ∑ n +4 n T 20=1504 T 30=3454 displaystyle∑ k =130 T k =35615 displaystyle∑ k =120 T k =10510

Q. Let $a_{1}, a_{2}, a_{3}, \dots$ be an arithmetic progression with $a_{1} = 7$ and common difference 8 . Let $T_{1}, T_{2}, T_{3}, \dots$ be such that $T_{1} = 3$ and $T_{n + 1} - T_{n} = a_{n}$ for $n \geq 1$ . Then, which of the following is/are TRUE ?

$T_{20} = 1604$

$k = 1 \sum 20 T_{k} = 10510$

$T_{30} = 3454$

$k = 1 \sum 30 T_{k} = 35610$

Q. Let a1​,a2​,a3​,… be an arithmetic progression with a1​=7 and common difference 8 . Let T1​,T2​,T3​,… be such that T1​=3 and Tn+1​−Tn​=an​ for n≥1. Then, which of the following is/are TRUE ?

T20​=1604

k=1∑20​Tk​=10510

T30​=3454

k=1∑30​Tk​=35610

Q. Let $a_{1}, a_{2}, a_{3}, \dots$ be an arithmetic progression with $a_{1} = 7$ and common difference 8 . Let $T_{1}, T_{2}, T_{3}, \dots$ be such that $T_{1} = 3$ and $T_{n + 1} - T_{n} = a_{n}$ for $n \geq 1$ . Then, which of the following is/are TRUE ?

$T_{20} = 1604$

$k = 1 \sum 20 T_{k} = 10510$

$T_{30} = 3454$

$k = 1 \sum 30 T_{k} = 35610$