Find the number of terms in the finite $A.P.$ $7, 11, 15, \ldots, 107$.
- A$11$
- B$15$
- C$45$
- D$26$
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Match the $APs$ given in column $A$ with suitable common differences given in column $B$.
Column $A$ Column $B$ $(A_{1}) \quad 2, -2, -6, -10, \ldots$ $(B_{1}) \quad \frac{2}{3}$ $(A_{2}) \quad a = -18, n = 10, a_{n} = 0$ $(B_{2}) \quad -5$ $(A_{3}) \quad a = 0, a_{10} = 6$ $(B_{3}) \quad 4$ $(A_{4}) \quad a_{2} = 13, a_{4} = 3$ $(B_{4}) \quad -4$ $(B_{5}) \quad 2$ $(B_{6}) \quad \frac{1}{2}$ $(B_{7}) \quad 5$
| Column $A$ | Column $B$ |
| $(A_{1}) \quad 2, -2, -6, -10, \ldots$ | $(B_{1}) \quad \frac{2}{3}$ |
| $(A_{2}) \quad a = -18, n = 10, a_{n} = 0$ | $(B_{2}) \quad -5$ |
| $(A_{3}) \quad a = 0, a_{10} = 6$ | $(B_{3}) \quad 4$ |
| $(A_{4}) \quad a_{2} = 13, a_{4} = 3$ | $(B_{4}) \quad -4$ |
| $(B_{5}) \quad 2$ | |
| $(B_{6}) \quad \frac{1}{2}$ | |
| $(B_{7}) \quad 5$ |
Difficult
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View SolutionHow many terms of the $A.P.$ $5, 8, 11, \dots$ add up to $670$?
Medium
View SolutionVerify that each of the following is an $AP$,and then write its next three terms.
$a, 2a+1, 3a+2, 4a+3, \ldots$
$a, 2a+1, 3a+2, 4a+3, \ldots$
Medium
View SolutionIn each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a = \frac{15}{2}, \quad d = \frac{3}{2}$
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